Homework 1 Due: Name. List the intercepts of the graph. 1) List the intercepts for the graph of the equation. 2) y2 = x + 1 2) 3) x2 + y - 9 = 0 3)

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1 Berkele Cit College Homework 1 Due: Precalculus w/ Analtic Geometr - Math 2 - Chapters 1-2 (half) Name List the intercepts of the graph. 1) 1) Objective: (1.2) Find Intercepts from a Graph List the intercepts for the graph of the equation. 2) 2 = + 1 2) Objective: (1.2) Find Intercepts from an Equation 3) = 0 3) Objective: (1.2) Find Intercepts from an Equation 4) = 4 4) Objective: (1.2) Find Intercepts from an Equation Instructor: K. Pernell 1

2 4 ) = ) Objective: (1.2) Find Intercepts from an Equation 6) = ) Objective: (1.2) Find Intercepts from an Equation Plot the point A. Plot the point B that has the given smmetr with point A. 7) A = (3, 2); B is smmetric to A with respect to the origin ) Objective: (1.2) Test an Equation for Smmetr with Respect to the -Ais, the -Ais, and the Origin 2

3 List the intercepts of the graph.tell whether the graph is smmetric with respect to the -ais, -ais, origin, or none of these. 8) 8) Objective: (1.2) Test an Equation for Smmetr with Respect to the -Ais, the -Ais, and the Origin 9) 9) Objective: (1.2) Test an Equation for Smmetr with Respect to the -Ais, the -Ais, and the Origin 3

4 Determine whether the graph of the equation is smmetric with respect to the -ais, the -ais, and/or the origin. ) = 2-9 ) 34 Objective: (1.2) Test an Equation for Smmetr with Respect to the -Ais, the -Ais, and the Origin Write the standard form of the equation of the circle. 11) 11) Objective: (1.4) Write the Standard Form of the Equation of a Circle Write the standard form of the equation of the circle with radius r and center (h, k). 12) r = 6; (h, k) = (2, -3) 12) Objective: (1.4) Write the Standard Form of the Equation of a Circle Find the center (h, k) and radius r of the circle with the given equation. 13) ( + )2 + ( - 8)2 = 81 13) Objective: (1.4) Write the Standard Form of the Equation of a Circle 4

5 14) 2 + ( + )2 = 0 14) Objective: (1.4) Write the Standard Form of the Equation of a Circle 1) ( + 6)2 + ( + 2)2 = 30 1) Objective: (1.4) Write the Standard Form of the Equation of a Circle Find the center (h, k) and radius r of the circle. Graph the circle. 16) = 0 16) Objective: (1.4) Work with the General Form of the Equation of a Circle

6 17) = 0 17) Objective: (1.4) Work with the General Form of the Equation of a Circle Find the center (h, k) and radius r of the circle with the given equation. 18) = ) Objective: (1.4) Work with the General Form of the Equation of a Circle Find the general form of the equation of the the circle. 19) Center at the point (2, -3); containing the point (, -3) 19) Objective: (1.4) Work with the General Form of the Equation of a Circle 6

7 Solve the problem. 20) A Ferris wheel has a diameter of 400 feet and the bottom of the Ferris wheel is 14 feet above the ground. Find the equation of the wheel if the origin is placed on the ground directl below the center of the wheel, as illustrated. 20) 400 ft. 14 ft. Objective: (1.4) Work with the General Form of the Equation of a Circle Determine whether the relation represents a function. If it is a function, state the domain and range. 21) 21) Alice Brad Carl snake cat dog Objective: (2.1) Determine Whether a Relation Represents a Function 22) 22) Alice Brad Carl cat dog Objective: (2.1) Determine Whether a Relation Represents a Function 7

8 23) {(41, -2), (, -1), (, 0), (6, 1), (14, 3)} 23) Objective: (2.1) Determine Whether a Relation Represents a Function Determine whether the equation defines as a function of. 24) = 1 24) Objective: (2.1) Determine Whether a Relation Represents a Function 2) = ± 1-6 2) Objective: (2.1) Determine Whether a Relation Represents a Function 26) = 2 26) Objective: (2.1) Determine Whether a Relation Represents a Function 27) = ) Objective: (2.1) Determine Whether a Relation Represents a Function Find the value for the function. 28) Find f(-1) when f() = ) Objective: (2.1) Find the Value of a Function 8

9 29) Find f(-) when f() = ) Objective: (2.1) Find the Value of a Function 30) Find f( - 1) when f() = ) Objective: (2.1) Find the Value of a Function 31) Find f( + h) when f() = ) Objective: (2.1) Find the Value of a Function Solve the problem. 32) If f() = - A and f() = -, what is the value of A? 32) + 1 Objective: (2.1) Find the Value of a Function 33) If a rock falls from a height of 90 meters on Earth, the height H (in meters) after seconds is approimatel H() = When does the rock strike the ground? Round to the nearest hundredth, if necessar. Objective: (2.1) Find the Value of a Function 33) Find the domain of the function. 3 34) g() = ) Objective: (2.1) Find the Domain of a Function Defined b an Equation 9

10 3) f() = 13-3) Objective: (2.1) Find the Domain of a Function Defined b an Equation 36) - 6 Objective: (2.1) Find the Domain of a Function Defined b an Equation 36) For the given functions f and g, find the requested function and state its domain. 37) f() = 9-9; g() = Find f + g. Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions 37) 38) f() = 7-4; g() = 9-9 Find f g. Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions 38) 39) f() = ; g() = ) Find f g. Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions 40) f() = + 11; g() = 4 40) Find f g. Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

11 Solve the problem. 41) Find (fg)(4) when f() = - 3 and g() = ) Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions 42) Find f g (-2) when f() = 2 - and g() = ) Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions f( + h) - f() Find and simplif the difference quotient of f,, h 0, for the function. h 43) f() = ) Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions 44) f() = 32 44) Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions Solve the problem. 4) Epress the gross salar G of a person who earns $ per hour as a function of the number of hours worked. Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions 4) 46) Jace, a commissioned salesperson, earns $370 base pa plus $30 per item sold. Epress Jaceʹs gross salar G as a function of the number of items sold. Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions 46) 11

12 Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if an, and an smmetr with respect to the -ais, the -ais, or the origin. 47) 47) Objective: (2.2) Identif the Graph of a Function 48) 48) Objective: (2.2) Identif the Graph of a Function 12

13 The graph of a function f is given. Use the graph to answer the question. 49) Is f(8) positive or negative? 49) - - Objective: (2.2) Obtain Information from or about the Graph of a Function 0) For what numbers is f() = 0? 0) - - Objective: (2.2) Obtain Information from or about the Graph of a Function 13

14 1) For what numbers is f() > 0? 1) Objective: (2.2) Obtain Information from or about the Graph of a Function Answer the question about the given function. 2) Given the function f() = , if = -1, what is f()? What point is on the graph of f? Objective: (2.2) Obtain Information from or about the Graph of a Function 2) 3) Given the function f() = 2 + 9, list the -intercept, if there is one, of the graph of f. 3) - 2 Objective: (2.2) Obtain Information from or about the Graph of a Function 14

15 The graph of a function is given. Decide whether it is even, odd, or neither. 4) ) Objective: (2.3) Determine Even and Odd Functions from a Graph ) ) Objective: (2.3) Determine Even and Odd Functions from a Graph 1

16 6) ) Objective: (2.3) Determine Even and Odd Functions from a Graph Determine algebraicall whether the function is even, odd, or neither. 7) f() = 3 7) Objective: (2.3) Identif Even and Odd Functions from the Equation 8) ) Objective: (2.3) Identif Even and Odd Functions from the Equation 9) f() = ) Objective: (2.3) Identif Even and Odd Functions from the Equation 60) f() = -4 60) Objective: (2.3) Identif Even and Odd Functions from the Equation 16

17 The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 61) (3, ) 61) Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant 62) (1, 2) 62) Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant 17

18 Use the graph to find the intervals on which it is increasing, decreasing, or constant. 63) 63) Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant For the function, find the average rate of change of f from 1 to : f() - f(1), ) f() = ) Objective: (2.3) Find the Average Rate of Change of a Function 6) f() = 6 + 6) Objective: (2.3) Find the Average Rate of Change of a Function Find the average rate of change for the function between the given values. 66) f() = 2 + 7; from 1 to 66) Objective: (2.3) Find the Average Rate of Change of a Function 18

19 67) f() = 2; from 2 to 8 67) Objective: (2.3) Find the Average Rate of Change of a Function 19

20 Answer Ke Testname: 13SPR_CH1 3_MATH2_HW_1 1) (-3, 0), (1, 0) (-, 0), (0, -3) 2) (0, -1), (-1, 0), (0, 1) 3) (-3, 0), (0, 9), (3, 0) 4) (-1, 0), (0, -2), (0, 2), (1, 0) ) (0, 0) 6) (-9, 0), (9, 0) 7) B ) intercepts: (-6, 0) and (6, 0) smmetric with respect to -ais, -ais, and origin 9) intercept: (0, 7) no smmetr ) -ais 11) ( - 3)2 + ( - 2)2 = 2 12) ( - 2)2 + ( + 3)2 = 36 13) (h, k) = (-, 8); r = 9 14) (h, k) = (0, -); r = 1) (h, k) = (-6, -2); r = 6 16) (h, k) = (, 2); r = A ) (h, k) = (-1, -3); r = ) (h, k) = (4, -8); r = 3 19) = 0 20) 2 + ( - 214)2 = 40,000 21) not a function 22) function domain: {Alice, Brad, Carl} range: {cat, dog} 23) not a function 24) function 2) not a function 26) not a function 27) function 28) ) ) ) h + 2h h ) A = ) 4.29 sec 34) { -, } 3) { 13} 36) { > 6} 37) (f + g)() = ; all real numbers 38) (f g)() = ; all real numbers 39) f g () = 4-9 ; 0, ) (f g)() = ; { -11, 0} 41) ) ) 8 44) 3(2+h) 4) G() = 46) G() =

21 Answer Ke Testname: 13SPR_CH1 3_MATH2_HW_1 47) not a function 48) function domain: all real numbers range: { 9} intercepts: (-4, 0), (0, 8), (2, 0) smmetr: none 49) positive 0) -6, 7, 1) [-0, -60), (70, 0) 2) 0; (-1, 0) 3) (0, ) 4) even ) neither 6) odd 7) odd 8) even 9) odd 60) odd 61) decreasing 62) increasing 63) Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1); constant on (-2, -1) and (1, 2) 64) ) ) 13 67)

Math 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 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