Section 1.1 Exercises
|
|
- Mervyn Tate
- 6 years ago
- Views:
Transcription
1 Section. Functions and Function Notation 99 Section. Eercises. The amount of garbage, G, produced by a city with population p is given by G f( p). G is measured in tons per week, and p is measured in thousands of people. a. The town of Tola has a population of 40,000 and produces tons of garbage each week. Epress this information in terms of the function f. b. Eplain the meaning of the statement f 5. The number of cubic yards of dirt, D, needed to cover a garden with area a square feet is given by D g( a). a. A garden with area 5000 ft requires 50 cubic yards of dirt. Epress this information in terms of the function g. b. Eplain the meaning of the statement g 00. Let f () t be the number of ducks in a lake t years after 990. Eplain the meaning of each statement: a. f 5 0 b. f Let ht () be the height above ground, in feet, of a rocket t seconds after launching. Eplain the meaning of each statement: a. 00 h 50 h b. 5. Select all of the following graphs which represent y as a function of. a b c d e f
2 400 Chapter 6. Select all of the following graphs which represent y as a function of. a b c d e f 7. Select all of the following tables which represent y as a function of. a b c y 8 4 y 8 8 y Select all of the following tables which represent y as a function of. a. 6 b. 6 6 c. 6 y 0 0 y 0 4 y Select all of the following tables which represent y as a function of. a. y b. y c. y d. y Select all of the following tables which represent y as a function of. a. y b. y c. y d. y
3 Section. Functions and Function Notation 40. Select all of the following tables which represent y as a function of and are one-toone. a. 8 b. 8 c. 8 8 y y 4 7 y 4 7. Select all of the following tables which represent y as a function of and are one-toone. a. 8 8 b. 8 4 c. 8 4 y 5 6 y y 5 6. Select all of the following graphs which are one-to-one functions. a. b. c. d. e. f. 4. Select all of the following graphs which are one-to-one functions. a b c d e f
4 40 Chapter Given the each function f ( ) graphed, evaluate f () and f () Given the function g ( ) graphed here, a. Evaluate g () b. Solve g 8. Given the function f ( ) graphed here. a. Evaluate f 4 b. Solve f( ) 4 9. Based on the table below, a. Evaluate f () b. Solve f ( ) f ( ) Based on the table below, a. Evaluate f (8) b. Solve f( ) f ( ) For each of the following functions, evaluate: f, f ( ), f (0), f (), and f (). f 4. f 8. f f f 6. f 5 7. f 8. f 4 9. f ( ) 0. f. f. f f. f 4.
5 Section. Functions and Function Notation Suppose f 8 4. Compute the following: a. f ( ) f () b. f ( ) f () 6. Suppose f. Compute the following: a. f ( ) f (4) b. f ( ) f (4) 7. Let f t t 5 a. Evaluate f (0) b. Solve f t 0 8. Let gp6 p a. Evaluate g (0) b. Solve g p 0 9. Match each function name with its equation. a. y i. Cube root b. y ii. Reciprocal c. y iii. Linear iv. Square Root d. y v. Absolute Value vi. Quadratic e. y vii. Reciprocal Squared f. y viii. Cubic g. y h. y 40. Match each graph with its equation. a. y b. y c. y d. y e. y f. y g. y h. y i. ii. iii. iv. v. vi. vii. viii.
6 404 Chapter 4. Match each table with its equation. a. y i. In Out b. y c. y 0 _ d. y / e. y f. y ii. In Out iii. In Out iv. In Out v. In Out - _ - _ vi. In Out Match each equation with its table a. Quadratic i. In Out b. Absolute Value c. Square Root d. Linear e. Cubic f. Reciprocal _ ii. In Out iii. In Out iv. In Out v. In Out - _ - _ Write the equation of the circle centered at (, 9 ) with radius Write the equation of the circle centered at (9, 8 ) with radius. vi. In Out Sketch a reasonable graph for each of the following functions. [UW] a. Height of a person depending on age. b. Height of the top of your head as you jump on a pogo stick for 5 seconds. c. The amount of postage you must put on a first class letter, depending on the weight of the letter.
7 Section. Functions and Function Notation Sketch a reasonable graph for each of the following functions. [UW] a. Distance of your big toe from the ground as you ride your bike for 0 seconds. b. You height above the water level in a swimming pool after you dive off the high board. c. The percentage of dates and names you ll remember for a history test, depending on the time you study 47. Using the graph shown, a. Evaluate f ( c ) b. Solve f p c. Suppose f b z. Find f ( z ) d. What are the coordinates of points L and K? a b c K t r p L f() 48. Dave leaves his office in Padelford Hall on his way to teach in Gould Hall. Below are several different scenarios. In each case, sketch a plausible (reasonable) graph of the function s = d(t) which keeps track of Dave s distance s from Padelford Hall at time t. Take distance units to be feet and time units to be minutes. Assume Dave s path to Gould Hall is long a straight line which is 400 feet long. [UW] a. Dave leaves Padelford Hall and walks at a constant spend until he reaches Gould Hall 0 minutes later. b. Dave leaves Padelford Hall and walks at a constant speed. It takes him 6 minutes to reach the half-way point. Then he gets confused and stops for minute. He then continues on to Gould Hall at the same constant speed he had when he originally left Padelford Hall. c. Dave leaves Padelford Hall and walks at a constant speed. It takes him 6 minutes to reach the half-way point. Then he gets confused and stops for minute to figure out where he is. Dave then continues on to Gould Hall at twice the constant speed he had when he originally left Padelford Hall.
8 406 Chapter d. Dave leaves Padelford Hall and walks at a constant speed. It takes him 6 minutes to reach the half-way point. Then he gets confused and stops for minute to figure out where he is. Dave is totally lost, so he simply heads back to his office, walking the same constant speed he had when he originally left Padelford Hall. e. Dave leaves Padelford heading for Gould Hall at the same instant Angela leaves Gould Hall heading for Padelford Hall. Both walk at a constant speed, but Angela walks twice as fast as Dave. Indicate a plot of distance from Padelford vs. time for the both Angela and Dave. f. Suppose you want to sketch the graph of a new function s = g(t) that keeps track of Dave s distance s from Gould Hall at time t. How would your graphs change in (a)-(e)?
9 Section. Domain and Range 407 Section. Eercises Write the domain and range of the function using interval notation... Write the domain and range of each graph as an inequality.. 4. Suppose that you are holding your toy submarine under the water. You release it and it begins to ascend. The graph models the depth of the submarine as a function of time. What is the domain and range of the function in the graph? 5. 6.
10 408 Chapter Find the domain of each function 7. f 8. f 5 9. f f 9 6. f. f 6 8. f 4 4. f f f 5 6 f f Given each function, evaluate: f ( ), f (0), f (), f (4) 7 if if 0 9. f 0. f 76 if 0 48 if 0. f. if 4 5 if 5 if 0 f if 0 if. f 4. 4 if if if 0 f 4 if 0 if
11 Section. Domain and Range 409 Write a formula for the piecewise function graphed below Sketch a graph of each piecewise function. f if 5 if. f 4 if 0 if 0. f 5. if 0 if 0 if f if if f if if if f if 0 if
12 40 Chapter Section. Eercises. The table below gives the annual sales (in millions of dollars) of a product. What was the average rate of change of annual sales a) Between 00 and 00 b) Between 00 and 004 year sales The table below gives the population of a town, in thousands. What was the average rate of change of population a) Between 00 and 004 b) Between 00 and 006 year population Based on the graph shown, estimate the average rate of change from = to = Based on the graph shown, estimate the average rate of change from = to = 5. Find the average rate of change of each function on the interval specified. 5. f ( ) on [, 5] 6. q( ) on [-4, ] 7. g ( ) on [-, ] k( t) 6t on [-, ] 0. t 4 h( ) 5 on [-, 4] t 4 p ( t) on [-, ] t Find the average rate of change of each function on the interval specified. Your answers will be epressions.. f ( ) 4 7 on [, b]. g ( ) 9 on [4, b]. h ( ) 4 on [, +h] 4. k ( ) 4 on [, +h] a ( t) on [9, 9+h] 6. b ( ) on [, +h] t 4 j( ) on [, +h] 8. r( t) 4t on [, +h] 9. f ( ) on [, +h] 0. g ( ) on [, +h]
13 Section. Rates of Change and Behavior of Graphs 4 For each function graphed, estimate the intervals on which the function is increasing and decreasing For each table below, select whether the table represents a function that is increasing or decreasing, and whether the function is concave up or concave down. 5. f() 6. g() 7. h() 8. k() f() g() h() k()
14 4 Chapter For each function graphed, estimate the intervals on which the function is concave up and concave down, and the location of any inflection points Use a graph to estimate the local etrema and inflection points of each function, and to estimate the intervals on which the function is increasing, decreasing, concave up, and concave down f ( ) h ( ) / 9. g ( t) t t 40. k( t) t t m ( ) n ( ) 8 8 6
15 Section.4 Composition of Functions 4 Section.4 Eercises Given each pair of equations, calculate f g 0 and g f 0. f 4 8, g7. f 5 7, g 4. f 4, g 4. f, g 4 Use the table of values to evaluate each epression 5. f( g (8)) 6. f g 5 7. g( f (5)) 8. g f 9. f( f (4)) 0. f f. gg ( ()) g g 6. f ( ) g( ) Use the graphs to evaluate the epressions below.. f( g ()) 4. f g 5. g( f ()) 6. g f 0 7. f( f (5)) 8. f f 4 9. gg ( ()) g g 0 0. For each pair of functions, find f g and g f. Simplify your answers. 4. f, g. f, g 4. f, g 4. f, g
16 44 Chapter 5. f, g5 6. f, g 4 7. If f 6, g ( ) 6 and h ( ), find f ( gh ( ( ))) 8. If f, g and h, find f ( gh ( ( ))) functions using interval notation. p a. Domain of m b. Domain of p( m ( )) c. Domain of mp ( ( )) 9. Given functions p and m functions using interval notation. q a. Domain of h b. Domain of qh ( ( )) c. Domain of hq ( ( )) 0. Given functions q and h 4, state the domains of the following 9, state the domains of the following. The function D( p ) gives the number of items that will be demanded when the price is p. The production cost, C ( ) is the cost of producing items. To determine the cost of production when the price is $6, you would do which of the following: a. Evaluate DC ( (6)) b. Evaluate CD ( (6)) c. Solve DC ( ( )) 6 d. Solve CDp ( ( )) 6. The function Ad ( ) gives the pain level on a scale of 0-0 eperienced by a patient with d milligrams of a pain reduction drug in their system. The milligrams of drug in the patient s system after t minutes is modeled by mt ( ). To determine when the patient will be at a pain level of 4, you would need to: a. Evaluate Am 4 b. Evaluate m A 4 c. Solve Amt d. Solve m Ad 4 4
17 Section.4 Composition of Functions 45. The radius r, in inches, of a balloon is related to the volume, V, by V rv ( ). Air 4 is pumped into the balloon, so the volume after t seconds is given by V t 0 0t a. Find the composite function rvt b. Find the time when the radius reaches 0 inches. 4. The number of bacteria in a refrigerated food product is given by NTT 56T, T where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by Tt ( ) 5t.5, where t is the time in hours. a. Find the composite function NTt b. Find the time when the bacteria count reaches 675 Find functions f ( ) and g ( ) so the given function can be epressed as h f g 5. h 6. h h 8. h 5 9. h 40. h 4 4. Let f ( ) be a linear function, having form [UW] f f is a linear function a. Show that b. Find a function g() such that 4. Let f [UW] a. Sketch the graphs of g g 6 8 f a b for constants a and b. f, f f, f f f on the interval 0. b. Your graphs should all intersect at the point (6, 6). The value = 6 is called a fied point of the function f()since f (6) 6 ; that is, 6 is fied - it doesn t move when f is applied to it. Give an eplanation for why 6 is a fied point for any function f( f( f(... f( )...))). c. Linear functions (with the eception of f ( ) ) can have at most one fied point. Quadratic functions can have at most two. Find the fied points of the function g. d. Give a quadratic function whose fied points are = and =.
18 46 Chapter 4. A car leaves Seattle heading east. The speed of the car in mph after m minutes is 70m given by the function Cm. [UW] 0 m a. Find a function m f() s that converts seconds s into minutes m. Write out the formula for the new function C( f( s )); what does this function calculate? b. Find a function m g( h) that converts hours h into minutes m. Write out the formula for the new function Cgh ( ( )) ; what does this function calculate? c. Find a function z v( s) that converts mph s into ft/sec z. Write out the formula for the new function vcm ( ( ) ; what does this function calculate?
19 Section.5 Transformation of Functions 47 Section.5 Eercises Describe how each function is a transformation of the original function f ( ). f 49. f( 4). f( ) 4. f( 4) 5. f 5 6. f 8 7. f 8. f 7 9. f 0.. Write a formula for f ( ). Write a formula for f ( ) f 4 shifted up unit and left units shifted down units and right unit. Write a formula for f( ) shifted down 4 units and right units 4. Write a formula for f( ) shifted up units and left 4 units 5. Tables of values for f ( ), g, ( ) and h ( ) are given below. Write g ( ) and h ( ) as transformations of f ( ) f() g() h() Tables of values for f ( ), g, ( ) and h ( ) are given below. Write g ( ) and h ( ) as transformations of f ( ) f() g() h() The graph of f is shown. Sketch a graph of each transformation of f ( ) 7. g 8. h 9. w 0. q
20 48 Chapter Sketch a graph of each function as a transformation of a toolkit function. f t ( t). h 4. k 4. mt t Write an equation for the function graphed below Find a formula for each of the transformations of the square root whose graphs are given below
21 Section.5 Transformation of Functions 49 The graph of f is shown. Sketch a graph of each transformation of f ( ). g. h. Starting with the graph of f 6 write the equation of the graph that results from a. reflecting f ( ) about the -ais and the y-ais b. reflecting f ( ) about the -ais, shifting left units, and down units 4. Starting with the graph of f 4 write the equation of the graph that results from a. reflecting f ( ) about the -ais b. reflecting f ( ) about the y-ais, shifting right 4 units, and up units Write an equation for the function graphed below
22 40 Chapter 9. For each equation below, determine if the function is Odd, Even, or Neither f a. 4 b. g ( ) c. h 40. For each equation below, determine if the function is Odd, Even, or Neither a. f b. 4 g h c. Describe how each function is a transformation of the original function f ( ) 4. f ( ) 4. f ( ) 4. 4 f ( ) f ( ) 45. f (5 ) 46. f ( ) 47. f 48. f 5 f 50. f ( ) Write a formula for f ( ) reflected over the y ais and horizontally compressed by a factor of 4 5. Write a formula for f ( ) reflected over the ais and horizontally stretched by a factor of 5. Write a formula for f( ) vertically compressed by a factor of, then shifted to the left units and down units. 54. Write a formula for f( ) vertically stretched by a factor of 8, then shifted to the right 4 units and up units. 55. Write a formula for f ( ) horizontally compressed by a factor of, then shifted to the right 5 units and up unit. 56. Write a formula for f ( ) horizontally stretched by a factor of, then shifted to the left 4 units and down units.
23 Section.5 Transformation of Functions 4 Describe how each formula is a transformation of a toolkit function. Then sketch a graph of the transformation. 57. f g ( ) h k 6. m 6. n 6. p 64. q 4 a b Determine the interval(s) on which the function is increasing and decreasing f g ( ) a k Determine the interval(s) on which the function is concave up and concave down 7. ( ) m 7. b 6 7. p k 74.
24 4 Chapter The function f ( ) is graphed here. Write an equation for each graph below as a transformation of f ( )
25 Section.5 Transformation of Functions 4 Write an equation for the transformed toolkit function graphed below
26 44 Chapter 99. Suppose you have a function y f( ) such that the domain of f ( ) is 6 and the range of f ( ) is y 5. [UW] a. What is the domain of f(( ))? b. What is the range of f ( ( ))? c. What is the domain of f( )? d. What is the range of f( )? e. Can you find constants B and C so that the domain of f ( B ( C)) is 8 9? f. Can you find constants A and D so that the range of Af( ) D is 0 y?
27 Section.6 Inverse Functions 45 Section.6 Eercises Assume that the function f is a one-to-one function.. If f (6) 7, find f (7). If f (), find f () f 4 8, find ( 8) f, find f ( ). If 5. If f 5, find f 5 7. Using the graph of f ( ) shown a. Find f 0 b. Solve f( ) 0 c. Find f 0 d. Solve f f 4. If 0 f, find f 6. If 4 8. Using the graph shown a. Find g () b. Solve g ( ) c. Find g () d. Solve g 9. Use the table below to fill in the missing values f() a. Find f b. Solve f( ) c. Find f 0 d. Solve f 7
28 46 Chapter 0. Use the table below to fill in the missing values. t h(t) a. Find h 6 b. Solve ht () 0 c. Find h 5 d. Solve h t For each table below, create a table for f() f f() For each function below, find f ( ). f 4. f 5 5. f 6. f 7. f f For each function, find a domain on which f is one-to-one and non-decreasing, then find the inverse of f restricted to that domain. 9. f 7 0. f 6 f 5. f.. If f 5 and g ( ) 5, find a. f ( g ( )) b. g( f( )) c. What does this tell us about the relationship between f ( ) and g? ( ) 4. If f( ) and a. f ( g ( )) b. g( f( )) g ( ), find c. What does this tell us about the relationship between f ( ) and g? ( )
Functions & Function Notation
Functions & Function Notation What is a Function? The natural world is full of relationships between quantities that change. When we see these relationships, it is natural for us to ask If I know one quantity,
More informationChapter 1: Functions. Section 1.1 Functions and Function Notation. Section 1.1 Functions and Function Notation 1
Section. Functions and Function Notation Chapter : Functions Section. Functions and Function Notation... Section. Domain and Range... Section. Rates of Change and Behavior of Graphs... 4 Section.4 Composition
More informationSection 1.4 Composition of Functions
Section.4 Composition of Functions 49 Section.4 Composition of Functions Suppose we wanted to calculate how much it costs to heat a house on a particular day of the year. The cost to heat a house will
More informationScottsdale Community College College Algebra Primary Authors Development Team
Scottsdale Community College College Algebra Primary Authors Development Team This tet is licensed under a Creative Commons Attribution-Share Alike 3.0 United States License. free to Share to Remi Attribution
More informationSolutions Manual for Precalculus An Investigation of Functions
Solutions Manual for Precalculus An Investigation of Functions David Lippman, Melonie Rasmussen nd Edition Solutions created at The Evergreen State College and Shoreline Community College Last edited 9/6/17
More information1.1 Functions. Input (Independent or x) and output (Dependent or y) of a function. Range: Domain: Function Rule. Input. Output.
1.1 Functions Function Function: A rule for a relationship between an input, or independent, quantity and an output, or dependent, quantity in which each input value uniquely determines one output value.
More informationChapter 1 Review Applied Calculus 7
Chapter Review Applied Calculus 7 Chapter : Review Section : Functions What is a Function? The natural world is full of relationships between quantities that change. When we see these relationships, it
More informationSolutions Manual for Precalculus An Investigation of Functions
Solutions Manual for Precalculus An Investigation of Functions David Lippman, Melonie Rasmussen 1 st Edition Solutions created at Te Evergreen State College and Soreline Community College 1.1 Solutions
More informationSolutions to Selected Exercises
59 Solutions to Selected Exercises Chapter Section.. a. f ( 0) = b. Tons of garbage per week is produced by a city with a population of 5,000.. a. In 995 there are 0 ducks in the lake b. In 000 there are
More informationOPEN ASSEMBLY EDITION
Business Calculus This document is attributed to Shana Calaway, Dale Hoffman and David Lippman Chapter OPEN ASSEMBLY EDITION OPEN ASSEMBLY editions of Open Tetbooks have been disaggregated into chapters
More informationCHAPTER 2 Differentiation
CHAPTER Differentiation Section. The Derivative and the Slope of a Graph............. 9 Section. Some Rules for Differentiation.................. 56 Section. Rates of Change: Velocit and Marginals.............
More informationSolutions to Selected Exercises
59 Solutions to Selected Exercises Chapter Section.. a. f 0 b. Tons of garbage per week is produced by a city with a population of 5,000.. a. In 995 there are 0 ducks in the lake b. In 000 there are 0
More informationThe questions listed below are drawn from midterm and final exams from the last few years at OSU. As the text book and structure of the class have
The questions listed below are drawn from midterm and final eams from the last few years at OSU. As the tet book and structure of the class have recently changed, it made more sense to list the questions
More informationAlgebra II Notes Rational Functions Unit Rational Functions. Math Background
Algebra II Notes Rational Functions Unit 6. 6.6 Rational Functions Math Background Previously, you Simplified linear, quadratic, radical and polynomial functions Performed arithmetic operations with linear,
More informationChapter 2: Differentiation 1. Find the slope of the tangent line to the graph of the function below at the given point.
Chapter : Differentiation 1. Find the slope of the tangent line to the graph of the function below at the given point. f( ) 10, (, ) 10 1 E) none of the above. Find the slope of the tangent line to the
More informationRelated Rates STEP 1 STEP 2:
Related Rates You can use derivative analysis to determine how two related quantities also have rates of change which are related together. I ll lead off with this example. 3 Ex) A spherical ball is being
More informationSection 1.3 Rates of Change and Behavior of Graphs
Section 1. Rates of Change and Behavior of Graphs 5 Section 1. Rates of Change and Behavior of Graphs Since functions represent how an output quantity varies with an input quantity, it is natural to ask
More informationCALCULUS I. Practice Problems. Paul Dawkins
CALCULUS I Practice Problems Paul Dawkins Table of Contents Preface... iii Outline... iii Review... Introduction... Review : Functions... Review : Inverse Functions... 6 Review : Trig Functions... 6 Review
More informationCHAPTER 1 Functions and Their Graphs
PART I CHAPTER Functions and Their Graphs Section. Lines in the Plane....................... Section. Functions........................... Section. Graphs of Functions..................... Section. Shifting,
More informationAll work must be shown in this course for full credit. Unsupported answers may receive NO credit.
AP Calculus.4 Worksheet All work must be shown in this course for full credit. Unsupported answers may receive NO credit.. What is a difference quotient?. How do you find the slope of a curve (aka slope
More informationUnit 7: Introduction to Functions
Section 7.1: Relations and Functions Section 7.2: Function Notation Section 7.3: Domain and Range Section 7.4: Practical Domain and Range Section 7.5: Applications KEY TERMS AND CONCEPTS Look for the following
More informationCalculus AB Semester 1 Final Review
Name Period Calculus AB Semester Final Review. Eponential functions: (A) kg. of a radioactive substance decay to kg. after years. Find how much remains after years. (B) Different isotopes of the same element
More informationThe Quadratic Formula
- The Quadratic Formula Content Standard Reviews A.REI..b Solve quadratic equations by... the quadratic formula... Objectives To solve quadratic equations using the Quadratic Formula To determine the number
More informationCHAPTER 3 Applications of Differentiation
CHAPTER Applications of Differentiation Section. Etrema on an Interval.............. 0 Section. Rolle s Theorem and the Mean Value Theorem. 07 Section. Increasing and Decreasing Functions and the First
More informationy=5 y=1+x 2 AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions
AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions. Which of the following integrals correctly corresponds to the area of the shaded region in the figure to the right? (A) (B) (C) (D) (E)
More informationAP Calculus BC Chapter 4 (A) 12 (B) 40 (C) 46 (D) 55 (E) 66
AP Calculus BC Chapter 4 REVIEW 4.1 4.4 Name Date Period NO CALCULATOR IS ALLOWED FOR THIS PORTION OF THE REVIEW. 1. 4 d dt (3t 2 + 2t 1) dt = 2 (A) 12 (B) 4 (C) 46 (D) 55 (E) 66 2. The velocity of a particle
More informationSection 3.4 Rational Functions
3.4 Rational Functions 93 Section 3.4 Rational Functions In the last few sections, we have built polynomials based on the positive whole number power functions. In this section we eplore functions based
More informationChapter 2 Analysis of Graphs of Functions
Chapter Analysis of Graphs of Functions Chapter Analysis of Graphs of Functions Covered in this Chapter:.1 Graphs of Basic Functions and their Domain and Range. Odd, Even Functions, and their Symmetry..
More informationDate: Pd: Unit 4. GSE H Analytic Geometry EOC Review Name: Units Rewrite ( 12 3) 2 in simplest form. 2. Simplify
GSE H Analytic Geometry EOC Review Name: Units 4 7 Date: Pd: Unit 4 1. Rewrite ( 12 3) 2 in simplest form. 2. Simplify 18 25 3. Which expression is equivalent to 32 8? a) 2 2 27 4. Which expression is
More informationSection 3.8 Inverses and Radical Functions
.8 Inverses and Radical Functions 9 Section.8 Inverses and Radical Functions In this section, we will explore the inverses of polynomial and rational functions, and in particular the radical functions
More informationHonors Math 2 Unit 5 Exponential Functions. *Quiz* Common Logs Solving for Exponents Review and Practice
Honors Math 2 Unit 5 Exponential Functions Notes and Activities Name: Date: Pd: Unit Objectives: Objectives: N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of
More informationFunctions. Introduction
Functions,00 P,000 00 0 970 97 980 98 990 99 000 00 00 Figure Standard and Poor s Inde with dividends reinvested (credit "bull": modification of work b Praitno Hadinata; credit "graph": modification of
More information3. If a coordinate is zero the point must be on an axis. If the x-coordinate is zero, where will the point be?
Chapter 2: Equations and Inequalities Section 1: The Rectangular Coordinate Systems and Graphs 1. Cartesian Coordinate System. 2. Plot the points ( 3, 5), (4, 3), (3, 4), ( 3, 0) 3. If a coordinate is
More informationSection 3.4 Rational Functions
88 Chapter 3 Section 3.4 Rational Functions In the last few sections, we have built polynomials based on the positive whole number power functions. In this section we eplore functions based on power functions
More informationFundamentals of Algebra, Geometry, and Trigonometry. (Self-Study Course)
Fundamentals of Algebra, Geometry, and Trigonometry (Self-Study Course) This training is offered eclusively through the Pennsylvania Department of Transportation, Business Leadership Office, Technical
More informationf on the same coordinate axes.
Calculus AB 0 Unit : Station Review # TARGETS T, T, T, T8, T9 T: A particle P moves along on a number line. The following graph shows the position of P as a function of t time S( cm) (0,0) (9, ) (, ) t
More informationMath 1050 REVIEW for Exam 1. Use synthetic division to find the quotient and the remainder. 1) x3 - x2 + 6 is divided by x + 2
Math 0 REVIEW for Eam 1 Use snthetic division to find the quotient and the remainder. 1) 3-2 + 6 is divided b + 2 Use snthetic division to determine whether - c is a factor of the given polnomial. 2) 3-32
More informationMAT 210 TEST 2 REVIEW (Ch 12 and 13)
Class: Date: MAT 0 TEST REVIEW (Ch and ) Multiple Choice Identify the choice that best completes the statement or answers the question.. The population P is currently 0,000 and growing at a rate of 7,000
More informationChapter 3: Polynomial and Rational Functions
Chapter 3: Polynomial and Rational Functions Section 3.1 Power Functions & Polynomial Functions... 155 Section 3. Quadratic Functions... 163 Section 3.3 Graphs of Polynomial Functions... 176 Section 3.4
More informationFunctions. Introduction CHAPTER OUTLINE
Functions,00 P,000 00 0 970 97 980 98 990 99 000 00 00 Figure Standard and Poor s Inde with dividends reinvested (credit "bull": modification of work b Praitno Hadinata; credit "graph": modification of
More information1. m = 3, P (3, 1) 2. m = 2, P ( 5, 8) 3. m = 1, P ( 7, 1) 4. m = m = 0, P (3, 117) 8. m = 2, P (0, 3)
. Linear Functions 69.. Eercises To see all of the help resources associated with this section, click OSttS Chapter. In Eercises - 0, find both the point-slope form and the slope-intercept form of the
More informationSection 1.2 Domain and Range
Section 1. Domain and Range 1 Section 1. Domain and Range One o our main goals in mathematics is to model the real world with mathematical unctions. In doing so, it is important to keep in mind the limitations
More informationMATH 112 Final Exam Study Questions
MATH Final Eam Study Questions Spring 08 Note: Certain eam questions have been more challenging for students. Questions marked (***) are similar to those challenging eam questions.. A company produces
More informationChapter Four. Chapter Four
Chapter Four Chapter Four CHAPTER FOUR 99 ConcepTests for Section 4.1 1. Concerning the graph of the function in Figure 4.1, which of the following statements is true? (a) The derivative is zero at two
More informationChapter 5: Trigonometric Functions of Angles
Chapter 5: Trigonometric Functions of Angles In the previous chapters we have explored a variety of functions which could be combined to form a variety of shapes. In this discussion, one common shape has
More informationFinal Exam Review Sheet Algebra for Calculus Fall Find each of the following:
Final Eam Review Sheet Algebra for Calculus Fall 007 Find the distance between each pair of points A) (,7) and (,) B), and, 5 5 Find the midpoint of the segment with endpoints (,) and (,) Find each of
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 8) Decreasing
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 8) Decreasing Find the open interval(s) where the function is changing as requested. 1) Decreasing; f()
More informationGraphing and Optimization
BARNMC_33886.QXD //7 :7 Page 74 Graphing and Optimization CHAPTER - First Derivative and Graphs - Second Derivative and Graphs -3 L Hôpital s Rule -4 Curve-Sketching Techniques - Absolute Maima and Minima
More informationCHAPTER 8 Quadratic Equations, Functions, and Inequalities
CHAPTER Quadratic Equations, Functions, and Inequalities Section. Solving Quadratic Equations: Factoring and Special Forms..................... 7 Section. Completing the Square................... 9 Section.
More informationCOMPOSITE AND INVERSE FUNCTIONS & PIECEWISE FUNCTIONS
Functions Modeling Change: A Preparation or Calculus, 4th Edition, 2011, Connally 2.4 COMPOSITE AND INVERSE FUNCTIONS & PIECEWISE FUNCTIONS Functions Modeling Change: A Preparation or Calculus, 4th Edition,
More informationIdentify the domain and the range of the relation from the graph. 8)
INTERMEDIATE ALGEBRA REVIEW FOR TEST Use the given conditions to write an equation for the line. 1) a) Passing through (, -) and parallel to = - +. b) Passing through (, 7) and parallel to - 3 = 10 c)
More informationx f(x)
CALCULATOR SECTION. For y + y = 8 find d point (, ) on the curve. A. B. C. D. dy at the 7 E. 6. Suppose silver is being etracted from a.t mine at a rate given by A'( t) = e, A(t) is measured in tons of
More informationMath Analysis Chapter 2 Notes: Polynomial and Rational Functions
Math Analysis Chapter Notes: Polynomial and Rational Functions Day 13: Section -1 Comple Numbers; Sections - Quadratic Functions -1: Comple Numbers After completing section -1 you should be able to do
More informationx f(x)
CALCULATOR SECTION. For y y 8 find d point (, ) on the curve. A. D. dy at the 7 E. 6. Suppose silver is being etracted from a.t mine at a rate given by A'( t) e, A(t) is measured in tons of silver and
More informationIn this section we want to apply what we have learned about functions to real world problems, a.k.a. word problems.
9.7 Applications of Functions In this section we want to apply what we have learned about functions to real world problems, a.k.a. word problems. There are two primary types of application problems we
More informationUnit #1 - Transformation of Functions, Exponentials and Logarithms
Unit #1 - Transformation of Functions, Exponentials and Logarithms Some problems and solutions selected or adapted from Hughes-Hallett Calculus. Note: This unit, being review of pre-calculus has substantially
More information3.1 Start Thinking. 3.1 Warm Up. 3.1 Cumulative Review Warm Up. Consider the equation y = x.
3.1 Start Thinking Consider the equation =. Are there an values of that ou cannot substitute into the equation? If so, what are the? Are there an values of that ou cannot obtain as an answer? If so, what
More informationc) domain {x R, x 3}, range {y R}
Answers Chapter 1 Functions 1.1 Functions, Domain, and Range 1. a) Yes, no vertical line will pass through more than one point. b) No, an vertical line between = 6 and = 6 will pass through two points..
More informationCHAPTER 2 Polynomial and Rational Functions
CHAPTER Polnomial and Rational Functions Section. Quadratic Functions..................... 9 Section. Polnomial Functions of Higher Degree.......... Section. Real Zeros of Polnomial Functions............
More informationMAC 2233, Survey of Calculus, Exam 3 Review This exam covers lectures 21 29,
MAC 2233, Survey of Calculus, Exam 3 Review This exam covers lectures 21 29, This review includes typical exam problems. It is not designed to be comprehensive, but to be representative of topics covered
More informationCalculus BC AP/Dual Fall Semester Review Sheet REVISED 1 Name Date. 3) Explain why f(x) = x 2 7x 8 is a guarantee zero in between [ 3, 0] g) lim x
Calculus BC AP/Dual Fall Semester Review Sheet REVISED Name Date Eam Date and Time: Read and answer all questions accordingly. All work and problems must be done on your own paper and work must be shown.
More informationAP Calculus AB/BC ilearnmath.net
CALCULUS AB AP CHAPTER 1 TEST Don t write on the test materials. Put all answers on a separate sheet of paper. Numbers 1-8: Calculator, 5 minutes. Choose the letter that best completes the statement or
More informationReview Sheet for Second Midterm Mathematics 1300, Calculus 1
Review Sheet for Second Midterm Mathematics 300, Calculus. For what values of is the graph of y = 5 5 both increasing and concave up? >. 2. Where does the tangent line to y = 2 through (0, ) intersect
More informationDoug Clark The Learning Center 100 Student Success Center learningcenter.missouri.edu Overview
Math 1400 Final Exam Review Saturday, December 9 in Ellis Auditorium 1:00 PM 3:00 PM, Saturday, December 9 Part 1: Derivatives and Applications of Derivatives 3:30 PM 5:30 PM, Saturday, December 9 Part
More informationSection 3.3 Graphs of Polynomial Functions
3.3 Graphs of Polynomial Functions 179 Section 3.3 Graphs of Polynomial Functions In the previous section we eplored the short run behavior of quadratics, a special case of polynomials. In this section
More informationMath 111 Final Exam Review KEY
Math 111 Final Eam Review KEY 1. Use the graph of y = f in Figure 1 to answer the following. Approimate where necessary. a Evaluate f 1. f 1 = 0 b Evaluate f0. f0 = 6 c Solve f = 0. =, = 1, =,or = 3 Solution
More informationSolutions to Intermediate and College Algebra by Rhodes
Solutions to Intermediate and College Algebra by Rhodes Section 1.1 1. 20 2. -21 3. 105 4. -5 5. 18 6. -3 7. 65/2 = 32.5 8. -36 9. 539 208 2.591 10. 13/3 11. 81 12. 60 = 2 15 7.746 13. -2 14. -1/3 15.
More informationAP Calculus (BC) Summer Assignment (169 points)
AP Calculus (BC) Summer Assignment (69 points) This packet is a review of some Precalculus topics and some Calculus topics. It is to be done NEATLY and on a SEPARATE sheet of paper. Use your discretion
More informationMATH 110: FINAL EXAM REVIEW
MATH 0: FINAL EXAM REVIEW Can you solve linear equations algebraically and check your answer on a graphing calculator? (.) () y y= y + = 7 + 8 ( ) ( ) ( ) ( ) y+ 7 7 y = 9 (d) ( ) ( ) 6 = + + Can you set
More informationMath 251 Final Exam Review Fall 2016
Below are a set of review problems that are, in general, at least as hard as the problems you will see on the final eam. You should know the formula for area of a circle, square, and triangle. All other
More information9-1. The Function with Equation y = ax 2. Vocabulary. Graphing y = x 2. Lesson
Chapter 9 Lesson 9-1 The Function with Equation = a BIG IDEA The graph of an quadratic function with equation = a, with a 0, is a parabola with verte at the origin. Vocabular parabola refl ection-smmetric
More informationPosition, Velocity, Acceleration
191 CHAPTER 7 Position, Velocity, Acceleration When we talk of acceleration we think of how quickly the velocity is changing. For example, when a stone is dropped its acceleration (due to gravity) is approximately
More information3 2 (C) 1 (D) 2 (E) 2. Math 112 Fall 2017 Midterm 2 Review Problems Page 1. Let. . Use these functions to answer the next two questions.
Math Fall 07 Midterm Review Problems Page Let f and g. Evaluate and simplify f g. Use these functions to answer the net two questions.. (B) (E) None of these f g. Evaluate and simplify. (B) (E). Consider
More informationAlgebra II Notes Unit Nine: Rational Equations and Functions
Syllabus Objectives: 9. The student will solve a problem by applying inverse and joint variation. 9.6 The student will develop mathematical models involving rational epressions to solve realworld problems.
More informationChapter 2: Quadratic and Other Special Functions. Exercises 2.1. x 2 11x 10 0 x 2 10x x ( x 10)(x 1) 0 x 10 0 or x 1 0
Mathematical Applications for the Management Life and Social Sciences 11th Edition Harshbarger SOLUTIONS MANUAL Full clear download at: https://testbankreal.com/download/mathematical-applications-managementlife-social-sciences-11th-edition-harshbarger-solutions-manual/
More informationAnswers Investigation 4
Answers Investigation Applications. a. 7 gallons are being pumped out each hour; students may make a table and notice the constant rate of change, which is - 7, or they may recognize that - 7 is the coefficient
More informationFLC Ch 1-3 (except 1.4, 3.1, 3.2) Sec 1.2: Graphs of Equations in Two Variables; Intercepts, Symmetry
Math 370 Precalculus [Note to Student: Read/Review Sec 1.1: The Distance and Midpoint Formulas] Sec 1.2: Graphs of Equations in Two Variables; Intercepts, Symmetry Defns A graph is said to be symmetric
More informationbe an nth root of a, and let m be a positive integer. ( ) ( )
Chapter 7: Power, Roots, and Radicals Chapter 7.1: Nth Roots and Rational Exponents Evaluating nth Roots: Relating Indices and Powers Real nth Roots: Let be an integer greater than 1 and let be a real
More informationName Class Date. Quadratic Functions and Transformations. 4 6 x
- Quadratic Functions and Transformations For Eercises, choose the correct letter.. What is the verte of the function 53()? D (, ) (, ) (, ) (, ). Which is the graph of the function f ()5(3) 5? F 6 6 O
More informationAP Calculus Free-Response Questions 1969-present AB
AP Calculus Free-Response Questions 1969-present AB 1969 1. Consider the following functions defined for all x: f 1 (x) = x, f (x) = xcos x, f 3 (x) = 3e x, f 4 (x) = x - x. Answer the following questions
More informationSyllabus Objective: 2.9 The student will sketch the graph of a polynomial, radical, or rational function.
Precalculus Notes: Unit Polynomial Functions Syllabus Objective:.9 The student will sketch the graph o a polynomial, radical, or rational unction. Polynomial Function: a unction that can be written in
More informationMultiplying Polynomials. The rectangle shown at the right has a width of (x + 2) and a height of (2x + 1).
Page 1 of 6 10.2 Multiplying Polynomials What you should learn GOAL 1 Multiply two polynomials. GOAL 2 Use polynomial multiplication in real-life situations, such as calculating the area of a window in
More informationCalculus 1st Semester Final Review
Calculus st Semester Final Review Use the graph to find lim f ( ) (if it eists) 0 9 Determine the value of c so that f() is continuous on the entire real line if f ( ), c /, > 0 Find the limit: lim 6+
More informationLESSON #24 - POWER FUNCTIONS COMMON CORE ALGEBRA II
1 LESSON #4 - POWER FUNCTIONS COMMON CORE ALGEBRA II Before we start to analze polnomials of degree higher than two (quadratics), we first will look at ver simple functions known as power functions. The
More informationCHAPTER 3 Applications of Differentiation
CHAPTER Applications of Differentiation Section. Etrema on an Interval.............. Section. Rolle s Theorem and the Mean Value Theorem. 7 Section. Increasing and Decreasing Functions and the First Derivative
More informationSection Functions and Function Notation
Section 1.1 - Functions and Function Notation A function is a relationship between two quantities. If the value of the first quantity determines exactly one value of the second quantity, we say the second
More informationStudents must be prepared to take a quiz on pre-calculus material by the 2 nd day of class.
AP Calculus AB Students must be prepared to take a quiz on pre-calculus material by the nd day of class. You must be able to complete each of these problems Uwith and without the use of a calculatoru (unless
More informationMATH 122 FALL Final Exam Review Problems
MATH 122 FALL 2013 Final Exam Review Problems Chapter 1 1. As a person hikes down from the top of a mountain, the variable t represents the time, in minutes, since the person left the top of the mountain,
More informationChapter 6 Overview: Applications of Derivatives
Chapter 6 Overview: Applications of Derivatives There are two main contets for derivatives: graphing and motion. In this chapter, we will consider the graphical applications of the derivative. Much of
More informationMat 210 Business Calculus Final Exam Review Spring Final on April 28 in COOR HALL 199 at 7:30 AM
f ( Mat Business Calculus Final Eam Review Spring Final on April 8 in COOR HALL 99 at 7: AM. A: Find the limit (if it eists) as indicated. Justify your answer. 8 a) lim (Ans: 6) b) lim (Ans: -) c) lim
More informationSection 3.1 Power Functions & Polynomial Functions
Chapter : Polynomial and Rational Functions Section. Power Functions & Polynomial Functions... 59 Section. Quadratic Functions... 67 Section. Graphs of Polynomial Functions... 8 Section.4 Factor Theorem
More information+ 2 on the interval [-1,3]
Section.1 Etrema on an Interval 1. Understand the definition of etrema of a function on an interval.. Understand the definition of relative etrema of a function on an open interval.. Find etrema on a closed
More informationCHAPTER 2 Differentiation
CHAPTER Differentiation Section. The Derivative and the Slope of a Graph............. 6 Section. Some Rules for Differentiation.................. 69 Section. Rates of Change: Velocit and Marginals.............
More informationMini-Lecture 8.1 Solving Quadratic Equations by Completing the Square
Mini-Lecture 8.1 Solving Quadratic Equations b Completing the Square Learning Objectives: 1. Use the square root propert to solve quadratic equations.. Solve quadratic equations b completing the square.
More information1 st Semester Final Review Date No
CHAPTER 1 REVIEW 1. Simplify the epression and eliminate any negative eponents. Assume that all letters denote positive numbers. r s 6r s. Perform the division and simplify. 6 8 9 1 10. Simplify the epression.
More informationMATH Calculus I - Prerequisite Review
MATH 241 - Calculus I - Prerequisite Review Give eact answers unless a problem specifies otherwise. + 5 1. Rationalize the numerator and simplify: 10 2. Simplify and give your answer in simplified radical
More informationChapter 1 Review Applied Calculus 31
Chapter Review Applied Calculus Section : Linear Functions As you hop into a taxicab in Allentown, the meter will immediately read $.0; this is the drop charge made when the taximeter is activated. After
More informationMath 111 Final Exam Review KEY
Math 111 Final Eam Review KEY 1. Use the graph of = f in Figure 1 to answer the following. Approimate where necessar. a b Evaluate f 1. f 1 = 0 Evaluate f0. f0 = 6 c Solve f = 0. =, = 1, =, or = 3 Solution
More informationApplications. 60 Say It With Symbols. g = 25 -
Applications 1. A pump is used to empt a swimming pool. The equation w =-275t + 1,925 represents the gallons of water w that remain in the pool t hours after pumping starts. a. How man gallons of water
More informationMath 120 Handouts. Functions Worksheet I (will be provided in class) Point Slope Equation of the Line 3. Functions Worksheet III 15
Math 0 Handouts HW # (will be provided to class) Lines: Concepts from Previous Classes (emailed to the class) Parabola Plots # (will be provided in class) Functions Worksheet I (will be provided in class)
More information