Unit 1: Functions, Equations, & Graphs

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Honors Algebra ~ Spring 014 Name: 0 Unit 1: Functions, Equations, & Graphs At the end of this unit, you will know how to: Identify functions Analyze transformations of functions Graph piecewise

1 Honors Algebra ~ Spring 014 Name: 0 Unit 1: Functions, Equations, & Graphs At the end of this unit, you will know how to: Identify functions Analyze transformations of functions Graph piecewise functions Graph and solve absolute value functions Write equations given real world data Graph two variable inequalities Make predictions from linear models Write solutions in interval notation Day DATE LESSON ASSIGNMENT 1 Wed. 1/ Class Policies and Procedures People Hunt Section -1: Relations & Functions Pg. 1 in packet, Get procedures sheet signed Register on blackboard and online textbook Complete Student info PRINT: Notes & packet Thurs. 1/3 Parent Functions, Domain/Range, and Shifts Transformations on Parent Functions Activity Packet p. 3 Fri. 1/4 Section 1-5: Absolute Value Equations and Inequalities Section.5: Absolute Value Graphs Section -6: Vertical & Horizontal Translations Packet Pg. 8 #10-1 Packet Pg. 9 #5 3 odd Packet Pg. 10 #1-6 4 Mon. 1/7 Function Poster Activity Review for Quiz on material from days 1-3 Study for Quiz on material from days Tues. 1/8 Quiz on material from days 1-3 Piecewise Functions Piecewise Handout 6 Wed. 1/9 Section -4: Using Linear Models/ Interpreting Slope of Linear Functions (Scatterplots, Linear Regression) Packet Pg. 3 7 Thurs. 1/30 Section -7: Two Variable Equations & Inequalities Review of absolute value equations and inequalities (Interval Notation & Matho) Packet Pg. 4 & 5 8 Fri. 1/31 Unit 1 TEST ACT Review: packet Pg. 7 Print Unit Notes & Packet from website!! Unit 1 Homework Grade:

Honors Algebra ~ Spring 014 1. Determine whether each relation is a function. Write yes or no. Identify the domain and range. a. b.

5, -0.3). State whether h will still be a function if each ordered pair given below is also included in h. a. (-, ) b. (0, 0) c.

The graph of each figure described below can be a function or a relation that is NOT a function depending on how it appears on a

2 Honors Algebra ~ Spring Determine whether each relation is a function. Write yes or no. Identify the domain and range. a. b. c. d. {(-3, 4), (4, ), (6, 4)} e. {(-8, 3), (, 5), (-1, 3), (, -4)}. A function h includes the ordered pairs (-, 1), (1, ), and (3.5, -0.3). State whether h will still be a function if each ordered pair given below is also included in h. a. (-, ) b. (0, 0) c. (, 1) 3. Find each value if f ( x ) 3x 5 and g( x ) x x 3. a. f(-3) b. g(3) c. g(a) d. f(x - 1) e. g(5n) f. g(a + 1) 4. The graph of each figure described below can be a function or a relation that is NOT a function depending on how it appears on a coordinate plane. Graph each figure as both a function and a relation that is NOT a function. a. set of ordered pairs b. a wavy line c. an angle 1

3 Honors Algebra ~ Spring 014 Day Homework: Parent Functions, Domain, and Range Part 1: Graph each of the following on your graphing calculator. State the domain and range of each relation in interval notation. Then state the parent function. 1. y x 8. y x y x 3x 4. y x 6 5. y x y x 1 Part : Graph each pair of functions on the same coordinate plane. Describe a transformation that changes f(x) to g(x). 7. f ( x ) x 1; g( x ) x 5 8. f ( x ) x 3; g( x ) x 4 9. f ( x ) x 3; g( x ) x f ( x ) x 1; g( x ) x Key Concept: Transformations of f(x) Vertical Translations Horizontal Translations Translation up k units, k > 0 y f ( x ) k Translation right h units, h > 0 y f ( x h) Translation down k units, k > 0 y f ( x ) k Translation left h units, h > 0 y f ( x h) Vertical Stretches and Compressions Reflections Vertical stretch, a > 1 y af ( x ) In the x-axis y f ( x ) Vertical compression, 0 < a < 1 y af ( x ) In the y-axis y f ( x )

4 Honors Algebra ~ Spring 014 Linear Regression Practice!! 1. The table shows the amount of trash produced in the United States from : YEAR Trash(millions of tons) a) Use your graphing calculator to find a prediction equation (line of best fit). Write your equation here. Let x = # of years since b) Predict the amount of trash in The table below shows the relationship between minutes spent studying and test scores. Study time (minutes) Test Score a) Determine the independent and dependent variables. b) Determine the equation for the line of best fit. c) Predict the test score of a person who studies for 60 minutes. 3. The table lists the price of a stamp from Let x=number of years since Year Stamp Cost a. Determine the equation for the line of best fit. b. Predict the cost of a stamp in 010. c. Is your answer in problem b realistic? Why or why not? d. According to your prediction equation, when will a stamp cost $.55? 3

5 Honors Algebra ~ Spring 014 Unit Test 1 Review Sheet 1. A study was conducted involving 0 students as they prepared for and took the Math section of the SAT Examination. Hrs. spent studying SAT scores a. Use your calculator to find a prediction equation for the data. b. Predict the SAT score for a student who studied 15 hours. c. Based on the above model, how many hours would a student need to study to get a 750 on the SAT?. The table below shows the relationship between calories and fat in fast-food hamburgers. Hamburger A B C D E F G H I Calories Fat a. Find a prediction equation for the data. b. A hamburger not on this list has 330 calories. About how much fat would you expect it to have? c. Based on your equation, would you expect a 470-calorie hamburger to have more or less than 7 g of fat? Would you expect a 650-calorie hamburger to have more or less than 33g of fat? 3. Solve & graph each equation or inequality. a. 4x 8 1 b. x 5 3x 4 c. 3x Determine if each relation is a function. a. {(3,4), (4,5), (5,6), (6,7), (7,8)} b. {(1,1), (1,), (1,3), (1,4), (1,5)} c. {(10,1), (9,1), (8,1), (7,1), (6,1)} d. {(-,4), (-3,9), (-4,16), (-5,5), (-6,36)} 5. Find: f a f x x x ( ) given ( ) 7 10 f ( 3) 6. If f ( a) a 16 and g( a) a a, find g() 7. Without graphing, identify the vertex of the graph y 3 x 4. How is the parent function y x transformed? 8. The graph of g(x) is the graph of f(x) = 4x compressed vertically by the factor 1 and then reflected in the y-axis. What is a function rule for g(x)? 9. What transformations change the graph of f(x) to the graph of g(x)? f x x g x x ( ) ( ) 6 1 4

Honors Algebra ~ Spring 014 10. Graph the following piecewise function: x 3 if x 1 f ( x) x 5 if 1 x x if x 11. Graph each of the following: a. y > 3x 6 b. x 3 1 y c. y 4x 4 1.

6 Honors Algebra ~ Spring Graph the following piecewise function: x 3 if x 1 f ( x) x 5 if 1 x x if x 11. Graph each of the following: a. y > 3x 6 b. x 3 1 y c. y 4x 4 1. Write the equation of the given graph. Write the domain and range in interval notation. a. b. 13. The graph shows an absolute value function after a translation 4 units up and 3 units left. Write the equation of the original equation. 5

Honors Algebra ~ Spring 014 Unit 1 Review Sheet Answers 1a) y = 3.8x + 363.4 b) 71 c) 16 hours a) y =.07x-9.7 b) 14.3 g c) 470 less (4g) 650 more (37g) 3. a) 9 7 x x OR x 4 4 b) x = 1 c) All reals 4.

7 Honors Algebra ~ Spring 014 Unit 1 Review Sheet Answers 1a) y = 3.8x b) 71 c) 16 hours a) y =.07x-9.7 b) 14.3 g c) 470 less (4g) 650 more (37g) 3. a) 9 7 x x OR x 4 4 b) x = 1 c) All reals 4.a) yes b) no c) yes d) yes 5. 4a 14a Vertex: (, 4). The parent is translated units to the right, vertically stretched by the factor of 3, and translated 4 units up. 8. g(x) = -x 9. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and then translated down 1 unit. 10. See teacher graph. 11)a) b) c) (line is dotted) 1a) Equation y x 5 b) Equation y x 3 4 Domain = all real numbers Range = 5 Domain = all real numbers y y Range = y y y x 7 6

8 Honors Algebra ~Spring 014 Honors Algebra ~ ACT Review #1 #1 For all y, ( y )( y 4)? # If x 3y 9, and x y 4, then y =? a y y y y ) 8 b) 8 c) 6 8 d y y y y ) 6 8 e) 6 8 f) 3 g) 1 h) 0 j) -1 k) -3 #3 If 3 a 1, which of the following Inequalities is FALSE? a a a a) a b) a c) a d) e) a a a 1 a #4 The relationship between temperature expressed in degrees Celisus and degrees Fahrenheit (F) is given by the formula: 5 C ( F 3) 9 If the temperature is -10 degrees Celsius, what is it in degrees Fahrenheit? 1 f) -50 g) 14 h) 3 j) k) 46 #5 What is the smallest value of x that satisfies the equation: x 9x 5 0? a) -5 b) -1 c) 1 d) 1 e) 5 #7 There are k students in a school. Of these, n% take at least one foreign language. Which of the following expressions represents the number of students who do NOT take a foreign language? a) (1 n) k b) (100 n) k c) (100 n) k nk d ) e) #9 If the arithmetic mean of four consecutive integers is 14.5, what is the smallest integer? a) 11 b) 1 c) 13 d) 14 e) 15 (1 nk ) 100 #6 Which of the following is equivalent to x 8 ( x 4)? f x x ) 3 4 g) 3 4 h) x 1 j x x ) 4 k) 4 #8 If the expression x 3px 10 when x = -1, what is the value of p? f ) g) - h) j) - k) #10 The sides of a triangle are in the ratio 4:3:. If the perimeter of the triangle is 79 units, what is the length of the smallest side? f) 88 g) 176 h) 00 j) 64 k) 35 7

9 Honors Algebra ~Spring 014 8

10 Honors Algebra ~Spring 014 9

11 Honors Algebra ~Spring

A. 16 B. 16 C. 4 D What is the solution set of 4x + 8 > 16?

A. 16 B. 16 C. 4 D What is the solution set of 4x + 8 > 16? Algebra II Honors Summer Math Packet 2017 Name: Date: 1. Solve for x: x + 6 = 5x + 12 2. What is the value of p in the equation 8p + 2 = p 10? F. 1 G. 1 H. J.. Solve for x: 15x (x + ) = 6 11. Solve for