practice and problem solving chapter 3

Algebra 2 Common Core

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Chapter 3 practice problems, chapter 3: functions, 3.1 relations and functions.

MAC1105 3_1 Practice Problems

MAC1105 3_1 Practice Problems Solutions

3.2 Properties of a Function’s Graph

MAC1105 3_2 Practice Problems

MAC1105 3_2 Practice Problems Solutions

3.3 Graphs of Basic Functions; Piecewise Functions

MAC1105 3_3 Practice Problems

MAC1105 3_3 Practice Problems Solutions

3.4 Transformations of Functions

MAC1105 3_4 Practice Problems

MAC1105 3_4 Practice Problems Solutions

3.5 The Algebra of Functions; Composite Functions

MAC1105 3_5 Practice Problems

MAC1105 3_5 Practice Problems Solutions

3.6 One-to-one Functions; Inverse Functions

MAC1105 3_6 Practice Problems

MAC1105 3_6 Practice Problems Solutions

The website of Professor Amanda Sartor

• Introduction
• 1.1 Use the Language of Algebra
• 1.2 Integers
• 1.3 Fractions
• 1.4 Decimals
• 1.5 Properties of Real Numbers
• Key Concepts

Review Exercises

Practice test.

• 2.1 Use a General Strategy to Solve Linear Equations
• 2.2 Use a Problem Solving Strategy
• 2.3 Solve a Formula for a Specific Variable
• 2.4 Solve Mixture and Uniform Motion Applications
• 2.5 Solve Linear Inequalities
• 2.6 Solve Compound Inequalities
• 2.7 Solve Absolute Value Inequalities
• 3.1 Graph Linear Equations in Two Variables
• 3.2 Slope of a Line
• 3.3 Find the Equation of a Line
• 3.4 Graph Linear Inequalities in Two Variables
• 3.5 Relations and Functions
• 3.6 Graphs of Functions
• 4.1 Solve Systems of Linear Equations with Two Variables
• 4.2 Solve Applications with Systems of Equations
• 4.3 Solve Mixture Applications with Systems of Equations
• 4.4 Solve Systems of Equations with Three Variables
• 4.5 Solve Systems of Equations Using Matrices
• 4.6 Solve Systems of Equations Using Determinants
• 4.7 Graphing Systems of Linear Inequalities
• 5.1 Add and Subtract Polynomials
• 5.2 Properties of Exponents and Scientific Notation
• 5.3 Multiply Polynomials
• 5.4 Dividing Polynomials
• Introduction to Factoring
• 6.1 Greatest Common Factor and Factor by Grouping
• 6.2 Factor Trinomials
• 6.3 Factor Special Products
• 6.4 General Strategy for Factoring Polynomials
• 6.5 Polynomial Equations
• 7.1 Multiply and Divide Rational Expressions
• 7.2 Add and Subtract Rational Expressions
• 7.3 Simplify Complex Rational Expressions
• 7.4 Solve Rational Equations
• 7.5 Solve Applications with Rational Equations
• 7.6 Solve Rational Inequalities
• 8.1 Simplify Expressions with Roots
• 8.2 Simplify Radical Expressions
• 8.3 Simplify Rational Exponents
• 8.4 Add, Subtract, and Multiply Radical Expressions
• 8.5 Divide Radical Expressions
• 8.6 Solve Radical Equations
• 8.7 Use Radicals in Functions
• 8.8 Use the Complex Number System
• 9.1 Solve Quadratic Equations Using the Square Root Property
• 9.2 Solve Quadratic Equations by Completing the Square
• 9.3 Solve Quadratic Equations Using the Quadratic Formula
• 9.4 Solve Quadratic Equations in Quadratic Form
• 9.5 Solve Applications of Quadratic Equations
• 9.6 Graph Quadratic Functions Using Properties
• 9.7 Graph Quadratic Functions Using Transformations
• 9.8 Solve Quadratic Inequalities
• 10.1 Finding Composite and Inverse Functions
• 10.2 Evaluate and Graph Exponential Functions
• 10.3 Evaluate and Graph Logarithmic Functions
• 10.4 Use the Properties of Logarithms
• 10.5 Solve Exponential and Logarithmic Equations
• 11.1 Distance and Midpoint Formulas; Circles
• 11.2 Parabolas
• 11.3 Ellipses
• 11.4 Hyperbolas
• 11.5 Solve Systems of Nonlinear Equations
• 12.1 Sequences
• 12.2 Arithmetic Sequences
• 12.3 Geometric Sequences and Series
• 12.4 Binomial Theorem

ⓐ yes, yes ⓑ yes, yes

ⓐ no, no ⓑ yes, yes

x -intercept: ( 2 , 0 ) , ( 2 , 0 ) , y -intercept: ( 0 , −2 ) ( 0 , −2 )

x -intercept: ( 3 , 0 ) , ( 3 , 0 ) , y -intercept: ( 0 , 2 ) ( 0 , 2 )

x -intercept: ( 4 , 0 ) , ( 4 , 0 ) , y -intercept: ( 0 , 12 ) ( 0 , 12 )

x -intercept: ( 8 , 0 ) , ( 8 , 0 ) , y -intercept: ( 0 , 2 ) ( 0 , 2 )

− 4 3 − 4 3

− 3 5 − 3 5

ⓐ m = 2 5 ; ( 0 , −1 ) m = 2 5 ; ( 0 , −1 ) ⓑ m = − 1 4 ; ( 0 , 2 ) m = − 1 4 ; ( 0 , 2 )

ⓐ m = − 4 3 ; ( 0 , 1 ) m = − 4 3 ; ( 0 , 1 ) ⓑ m = − 3 2 ; ( 0 , 6 ) m = − 3 2 ; ( 0 , 6 )

ⓐ intercepts ⓑ horizontal line ⓒ slope-intercept ⓓ vertical line

ⓐ vertical line ⓑ slope-intercept ⓒ horizontal line ⓓ intercepts

ⓐ 50 inches ⓑ 66 inches ⓒ The slope, 2, means that the height, h , increases by 2 inches when the shoe size, s , increases by 1. The h -intercept means that when the shoe size is 0, the height is 50 inches. ⓓ

ⓐ 40 degrees ⓑ 65 degrees ⓒ The slope, 1 4 , 1 4 , means that the temperature Fahrenheit ( F ) increases 1 degree when the number of chirps, n , increases by 4. The T -intercept means that when the number of chirps is 0, the temperature is 40°. ⓓ

ⓐ $25 ⓑ $85 ⓒ The slope, 4, means that the weekly cost, C , increases by $4 when the number of pizzas sold, p, increases by 1. The C -intercept means that when the number of pizzas sold is 0, the weekly cost is $25. ⓓ

ⓐ $35 ⓑ $170 ⓒ The slope, 1.8 , 1.8 , means that the weekly cost, C , increases by $ 1.80 $ 1.80 when the number of invitations, n , increases by 1. The C -intercept means that when the number of invitations is 0, the weekly cost is $35. ⓓ

ⓐ parallel ⓑ not parallel; same line

ⓐ parallel ⓑ parallel

ⓐ perpendicular ⓑ not perpendicular

y = 2 5 x + 4 y = 2 5 x + 4

y = − x − 3 y = − x − 3

y = 3 5 x + 1 y = 3 5 x + 1

y = 4 3 x − 5 y = 4 3 x − 5

y = − 2 5 x − 1 y = − 2 5 x − 1

y = − 3 4 x − 4 y = − 3 4 x − 4

y = 8 y = 8

y = 4 y = 4

y = 1 3 x − 10 3 y = 1 3 x − 10 3

y = − 2 5 x − 23 5 y = − 2 5 x − 23 5

x = 5 x = 5

x = −4 x = −4

y = 3 x − 10 y = 3 x − 10

y = 1 2 x + 1 y = 1 2 x + 1

y = − 1 3 x + 10 3 y = − 1 3 x + 10 3

y = −2 x + 16 y = −2 x + 16

y = −5 y = −5

y = −1 y = −1

x = −5 x = −5

ⓐ yes ⓑ yes ⓒ yes ⓓ yes ⓔ no

ⓐ yes ⓑ yes ⓒ no ⓓ no ⓔ yes

y ≥ −2 x + 3 y ≥ −2 x + 3

y ≤ 1 2 x − 4 y ≤ 1 2 x − 4

x − 4 y ≤ 8 x − 4 y ≤ 8

3 x − y ≥ 6 3 x − y ≥ 6

All points in the shaded region and on the boundary line, represent the solutions to y > 5 2 x − 4 . y > 5 2 x − 4 .

All points in the shaded region, but not those on the boundary line, represent the solutions to y < 2 3 x − 5 . y < 2 3 x − 5 .

All points in the shaded region, but not those on the boundary line, represent the solutions to 2 x − 3 y < 6 . 2 x − 3 y < 6 .

All points in the shaded region, but not those on the boundary line, represent the solutions to 2 x − y > 3 . 2 x − y > 3 .

All points in the shaded region, but not those on the boundary line, represent the solutions to y > − 3 x . y > − 3 x .

All points in the shaded region and on the boundary line, represent the solutions to y ≥ −2 x . y ≥ −2 x .

All points in the shaded region, but not those on the boundary line, represent the solutions to y < 5 . y < 5 .

All points in the shaded region and on the boundary line represent the solutions to y ≤ −1 . y ≤ −1 .

ⓐ 10 x + 13 y ≥ 260 10 x + 13 y ≥ 260 ⓑ

ⓒ Answers will vary.

ⓐ 10 x + 17.5 y ≥ 280 10 x + 17.5 y ≥ 280 ⓑ

ⓐ { 1 , 2 , 3 , 4 , 5 } { 1 , 2 , 3 , 4 , 5 } ⓑ { 1 , 8 , 27 , 64 , 125 } { 1 , 8 , 27 , 64 , 125 }

ⓐ { 1 , 2 , 3 , 4 , 5 } { 1 , 2 , 3 , 4 , 5 } ⓑ { 3 , 6 , 9 , 12 , 15 } { 3 , 6 , 9 , 12 , 15 }

ⓐ (Khanh Nguyen, kn68413), (Abigail Brown, ab56781), (Sumantha Mishal, sm32479), (Jose Hern and ez, jh47983) ⓑ {Khanh Nguyen, Abigail Brown, Sumantha Mishal, Jose Hern and ez} ⓒ {kn68413, ab56781, sm32479, jh47983}

ⓐ (Maria, November 6), (Arm and o, January 18), (Cynthia, December 8), (Kelly, March 15), (Rachel, November 6) ⓑ {Maria, Arm and o, Cynthia, Kelly, Rachel} ⓒ {November 6, January 18, December 8, March 15}

ⓐ ( −3 , 3 ) , ( −2 , 2 ) , ( −1 , 0 ) , ( −3 , 3 ) , ( −2 , 2 ) , ( −1 , 0 ) , ( 0 , −1 ) , ( 2 , −2 ) , ( 4 , −4 ) ( 0 , −1 ) , ( 2 , −2 ) , ( 4 , −4 ) ⓑ { −3 , −2 , −1 , 0 , 2 , 4 } { −3 , −2 , −1 , 0 , 2 , 4 } ⓒ { 3 , 2 , 0 , −1 , −2 , −4 } { 3 , 2 , 0 , −1 , −2 , −4 }

ⓐ ( −3 , 0 ) , ( −3 , 5 ) , ( −3 , −6 ) , ( −3 , 0 ) , ( −3 , 5 ) , ( −3 , −6 ) , ( −1 , −2 ) , ( 1 , 2 ) , ( 4 , −4 ) ( −1 , −2 ) , ( 1 , 2 ) , ( 4 , −4 ) ⓑ { −3 , −1 , 1 , 4 } { −3 , −1 , 1 , 4 } ⓒ { −6 , 0 , 5 , −2 , 2 , −4 } { −6 , 0 , 5 , −2 , 2 , −4 }

ⓐ Yes; { −3 , −2 , −1 , 0 , 1 , 2 , 3 } ; { −3 , −2 , −1 , 0 , 1 , 2 , 3 } ; { −6 , −4 , −2 , 0 , 2 , 4 , 6 } { −6 , −4 , −2 , 0 , 2 , 4 , 6 } ⓑ No; { 0 , 2 , 4 , 8 } ; { 0 , 2 , 4 , 8 } ; { −4 , −2 , −1 , 0 , 1 , 2 , 4 } { −4 , −2 , −1 , 0 , 1 , 2 , 4 }

ⓐ No; { 0 , 1 , 8 , 27 } ; { 0 , 1 , 8 , 27 } ; { −3 , −2 , −1 , 0 , 2 , 2 , 3 } { −3 , −2 , −1 , 0 , 2 , 2 , 3 } ⓑ Yes; { 7 , −5 , 8 , 0 , −6 , −2 , −1 } ; { 7 , −5 , 8 , 0 , −6 , −2 , −1 } ; { −3 , −4 , 0 , 4 , 2 , 3 } { −3 , −4 , 0 , 4 , 2 , 3 }

ⓐ no ⓑ {NBC, HGTV, HBO} ⓒ {Ellen Degeneres Show, Law and Order, Tonight Show, Property Brothers, House Hunters, Love it or List it, Game of Thrones, True Detective, Sesame Street}

ⓐ No ⓑ {Neal, Krystal, Kelvin, George, Christa, Mike} ⓒ {123-567-4839 work, 231-378-5941 cell, 743-469-9731 cell, 567-534-2970 work, 684-369-7231 cell, 798-367-8541 cell, 639-847-6971 cell}

ⓐ yes ⓑ no ⓒ yes

ⓐ no ⓑ yes ⓒ yes

ⓐ f ( 3 ) = 22 f ( 3 ) = 22 ⓑ f ( −1 ) = 6 f ( −1 ) = 6 ⓒ f ( t ) = 3 t 2 − 2 t − 1 f ( t ) = 3 t 2 − 2 t − 1

ⓐ ( 2 ) = 13 ( 2 ) = 13 ⓑ f ( −3 ) = 3 f ( −3 ) = 3 ⓒ f ( h ) = 2 h 2 + 4 h − 3 f ( h ) = 2 h 2 + 4 h − 3

ⓐ 4 m 2 − 7 4 m 2 − 7 ⓑ 4 x − 19 4 x − 19 ⓒ x − 12 x − 12

ⓐ 2 k 2 + 1 2 k 2 + 1 ⓑ 2 x + 3 2 x + 3 ⓒ 2 x + 4 2 x + 4

ⓐ t IND; N DEP ⓑ 205; the number of unread emails in Bryan’s account on the seventh day.

ⓐ t IND; N DEP ⓑ 460; the number of unread emails in Anthony’s account on the fourteenth day

The domain is [ −5 , 1 ] . [ −5 , 1 ] . The range is [ −4 , 2 ] . [ −4 , 2 ] .

The domain is [ −2 , 4 ] . [ −2 , 4 ] . The range is [ −5 , 3 ] . [ −5 , 3 ] .

ⓐ f ( 0 ) = 0 f ( 0 ) = 0 ⓑ f = ( π 2 ) = 2 f = ( π 2 ) = 2 ⓒ f = ( −3 π 2 ) = 2 f = ( −3 π 2 ) = 2 ⓓ f ( x ) = 0 f ( x ) = 0 for x = −2 π , − π , 0 , π , 2 π x = −2 π , − π , 0 , π , 2 π ⓔ ( −2 π , 0 ) , ( − π , 0 ) , ( 0 , 0 ) , ( π , 0 ) , ( 2 π , 0 ) ( −2 π , 0 ) , ( − π , 0 ) , ( 0 , 0 ) , ( π , 0 ) , ( 2 π , 0 ) ⓕ ( 0 , 0 ) ( 0 , 0 ) ⓖ [ −2 π , 2 π ] [ −2 π , 2 π ] ⓗ [ −2 , 2 ] [ −2 , 2 ]

ⓐ f ( 0 ) = 1 f ( 0 ) = 1 ⓑ f ( π ) = −1 f ( π ) = −1 ⓒ f ( − π ) = −1 f ( − π ) = −1 ⓓ f ( x ) = 0 f ( x ) = 0 for x = − 3 π 2 , − π 2 , π 2 , 3 π 2 x = − 3 π 2 , − π 2 , π 2 , 3 π 2 ⓔ ( −2 pi , 0 ) , ( −pi , 0 ) , ( 0 , 0 ) , ( pi , 0 ) , ( 2 pi , 0 ) ( −2 pi , 0 ) , ( −pi , 0 ) , ( 0 , 0 ) , ( pi , 0 ) , ( 2 pi , 0 ) ⓕ ( 0 , 1 ) ( 0 , 1 ) ⓖ [ −2 pi , 2 pi ] [ −2 pi , 2 pi ] ⓗ [ −1 , 1 ] [ −1 , 1 ]

Section 3.1 Exercises

ⓐ A: yes, B: no, C: yes, D: yes ⓑ A: yes, B: no, C: yes, D: yes

ⓐ A: yes, B: yes, C: yes, D: no ⓑ A: yes, B: yes, C: yes, D: no

( 3 , 0 ) , ( 0 , 3 ) ( 3 , 0 ) , ( 0 , 3 )

( 5 , 0 ) , ( 0 , −5 ) ( 5 , 0 ) , ( 0 , −5 )

( 2 , 0 ) , ( 0 , 6 ) ( 2 , 0 ) , ( 0 , 6 )

( 2 , 0 ) , ( 0 , −8 ) ( 2 , 0 ) , ( 0 , −8 )

( 5 , 0 ) , ( 0 , 2 ) ( 5 , 0 ) , ( 0 , 2 )

Answers will vary.

Section 3.2 Exercises

− 1 3 − 1 3

− 5 2 − 5 2

− 8 7 − 8 7

m = −7 ; ( 0 , 3 ) m = −7 ; ( 0 , 3 )

m = −3 ; ( 0 , 5 ) m = −3 ; ( 0 , 5 )

m = − 3 2 ; ( 0 , 3 ) m = − 3 2 ; ( 0 , 3 )

m = 5 2 ; ( 0 , −3 ) m = 5 2 ; ( 0 , −3 )

vertical line

slope-intercept

ⓐ $31 ⓑ $52 ⓒ The slope, 1.75 , 1.75 , means that the payment, P , increases by $ 1.75 $ 1.75 when the number of units of water used, w, increases by 1. The P -intercept means that when the number units of water Tuyet used is 0, the payment is $31. ⓓ

ⓐ $42 ⓑ $168.50 ⓒ The slope, 0.575 means that the amount he is reimbursed, R , increases by $0.575 when the number of miles driven, m, increases by 1. The R -intercept means that when the number miles driven is 0, the amount reimbursed is $42. ⓓ

ⓐ $400 ⓑ $940 ⓒ The slope, 0.15 , 0.15 , means that Cherie’s salary, S , increases by $0.15 for every $1 increase in her sales. The S -intercept means that when her sales are $0, her salary is $400. ⓓ

ⓐ $1570 ⓑ $5690 ⓒ The slope gives the cost per guest. The slope, 28, means that the cost, C , increases by $28 when the number of guests increases by 1. The C -intercept means that if the number of guests was 0, the cost would be $450. ⓓ

perpendicular

Section 3.3 Exercises

y = 3 x + 5 y = 3 x + 5

y = −3 x − 1 y = −3 x − 1

y = 1 5 x − 5 y = 1 5 x − 5

y = 3 x − 5 y = 3 x − 5

y = 1 2 x − 3 y = 1 2 x − 3

y = − 4 3 x + 3 y = − 4 3 x + 3

y = −2 y = −2

y = 5 8 x − 2 y = 5 8 x − 2

y = − 3 5 x + 1 y = − 3 5 x + 1

y = − 3 2 x + 9 y = − 3 2 x + 9

y = −7 x − 10 y = −7 x − 10

y = 5 y = 5

y = −7 y = −7

y = − x + 8 y = − x + 8

y = 1 4 x − 13 4 y = 1 4 x − 13 4

y = 2 x + 5 y = 2 x + 5

y = − 7 2 x + 4 y = − 7 2 x + 4

x = 7 x = 7

y = −4 y = −4

y = 4 x − 2 y = 4 x − 2

y = 2 x − 6 y = 2 x − 6

x = −3 x = −3

y = − 4 3 x y = − 4 3 x

y = − 3 2 x + 5 y = − 3 2 x + 5

y = 5 2 x y = 5 2 x

x = −2 x = −2

y = − 1 2 x + 5 y = − 1 2 x + 5

y = 1 6 x y = 1 6 x

y = − 4 3 x − 3 y = − 4 3 x − 3

y = − 3 4 x + 1 y = − 3 4 x + 1

y = − 1 5 x − 23 5 y = − 1 5 x − 23 5

y = −2 x − 2 y = −2 x − 2

Section 3.4 Exercises

ⓐ yes ⓑ yes ⓒ no ⓓ no ⓔ no

ⓐ no ⓑ no ⓒ yes ⓓ yes ⓔ no

ⓐ yes ⓑ no ⓒ no ⓓ no ⓔ no

y ≤ 3 x − 4 y ≤ 3 x − 4

y ≤ − 1 2 x + 1 y ≤ − 1 2 x + 1

x + y ≥ 5 x + y ≥ 5

3 x − y ≤ 6 3 x − y ≤ 6

ⓐ 11 x + 16.5 y ≥ 330 11 x + 16.5 y ≥ 330 ⓑ

ⓐ 15 x + 10 y ≥ 500 15 x + 10 y ≥ 500 ⓑ

Section 3.5 Exercises

ⓐ {1, 2, 3, 4, 5} ⓑ {4, 8, 12, 16, 20}

ⓐ {1, 5, 7, −2} ⓑ {7, 3, 9, −3, 8}

ⓐ (Rebecca, January 18), (Jennifer, April 1), (John, January 18), (Hector, June 23), (Luis, February 15), (Ebony, April 7), (Raphael, November 6), (Meredith, August 19), (Karen, August 19), (Joseph, July 30) ⓑ {Rebecca, Jennifer, John, Hector, Luis, Ebony, Raphael, Meredith, Karen, Joseph} ⓒ {January 18, April 1, June 23, February 15, April 7, November 6, August 19, July 30}

ⓐ (+100, 17. 2), (110, 18.9), (120, 20.6), (130, 22.3), (140, 24.0), (150, 25.7), (160, 27.5) ⓑ {+100, 110, 120, 130, 140, 150, 160,} ⓒ {17.2, 18.9, 20.6, 22.3, 24.0, 25.7, 27.5}

ⓐ (2, 3), (4, −3), (−2, −1), (−3, 4), (4, −1), (0, −3) ⓑ {−3, −2, 0, 2, 4} ⓒ {−3, −1, 3, 4}

ⓐ (1, 4), (1, −4), (−1, 4), (−1, −4), (0, 3), (0, −3) ⓑ {−1, 0, 1} ⓒ {−4, −3, 3,4}

ⓐ yes ⓑ {−3, −2, −1, 0, 1, 2, 3} ⓒ {9, 4, 1, 0}

ⓐ yes ⓑ {−3, −2, −1, 0, 1, 2, 3} ⓒ 0, 1, 8, 27}

ⓐ yes ⓑ {−3, −2, −1, 0, 1, 2, 3} ⓒ {0, 1, 2, 3}

ⓐ no ⓑ {Jenny, R and y, Dennis, Emily, Raul} ⓒ {RHern and [email protected], [email protected], [email protected], ESmi[email protected], [email protected], [email protected], R and [email protected]}

ⓐ yes ⓑ yes ⓒ no

ⓐ f ( 2 ) = 7 f ( 2 ) = 7 ⓑ f ( −1 ) = −8 f ( −1 ) = −8 ⓒ f ( a ) = 5 a − 3 f ( a ) = 5 a − 3

ⓐ f ( 2 ) = −6 f ( 2 ) = −6 ⓑ f ( −1 ) = 6 f ( −1 ) = 6 ⓒ f ( a ) = −4 a + 2 f ( a ) = −4 a + 2

ⓐ f ( 2 ) = 5 f ( 2 ) = 5 ⓑ f ( −1 ) = 5 f ( −1 ) = 5 ⓒ f ( a ) = a 2 − a + 3 f ( a ) = a 2 − a + 3

ⓐ f ( 2 ) = 9 f ( 2 ) = 9 ⓑ f ( −1 ) = 6 f ( −1 ) = 6 ⓒ f ( a ) = 2 a 2 − a + 3 f ( a ) = 2 a 2 − a + 3

ⓐ g ( h 2 ) = 2 h 2 + 1 g ( h 2 ) = 2 h 2 + 1 ⓑ g ( x + 2 ) = 2 x + 5 g ( x + 2 ) = 2 x + 5 ⓒ g ( x ) + g ( 2 ) = 2 x + 6 g ( x ) + g ( 2 ) = 2 x + 6

ⓐ g ( h 2 ) = −3 h 2 − 2 g ( h 2 ) = −3 h 2 − 2 ⓑ g ( x + 2 ) = −3 x − 8 g ( x + 2 ) = −3 x − 8 ⓒ g ( x ) + g ( 2 ) = −3 x − 10 g ( x ) + g ( 2 ) = −3 x − 10

ⓐ g ( h 2 ) = 3 − h 2 g ( h 2 ) = 3 − h 2 ⓑ g ( x + 2 ) = 1 − x g ( x + 2 ) = 1 − x ⓒ g ( x ) + g ( 2 ) = 4 − x g ( x ) + g ( 2 ) = 4 − x

ⓐ t IND; N DEP ⓑ N ( 4 ) = 165 N ( 4 ) = 165 the number of unwatched shows in Sylvia’s DVR at the fourth week.

ⓐ x IND; C DEP ⓑ N ( 0 ) = 1500 N ( 0 ) = 1500 the daily cost if no books are printed ⓒ N ( 1000 ) = 4750 N ( 1000 ) = 4750 the daily cost of printing 1000 books

Section 3.6 Exercises

ⓑ D:(-∞,∞), R:(-∞,∞)

ⓑ D:(-∞,∞), R:{5}

ⓑ D:(-∞,∞), R: { −3 } { −3 }

ⓑ D:(-∞,∞), R:[0,∞)

ⓑ (-∞,∞), R:(-∞,0]

ⓑ (-∞,∞), R:[-∞,0)

ⓑ (-∞,∞), R:[ −1 , −1 , ∞)

ⓑ D:[0,∞), R:[0,∞)

ⓑ D:[1,∞), R:[0,∞)

ⓑ D:[ −1 , −1 , ∞), R:[−∞,∞)

ⓑ D:(-∞,∞), R:[1,∞)

D: [2,∞), R: [0,∞)

D: (-∞,∞), R: [4,∞)

D: [ −2 , 2 ] , [ −2 , 2 ] , R: [0, 2]

ⓐ f ( 0 ) = 0 f ( 0 ) = 0 ⓑ ( pi / 2 ) = −1 ( pi / 2 ) = −1 ⓒ f ( −3 pi / 2 ) = −1 f ( −3 pi / 2 ) = −1 ⓓ f ( x ) = 0 f ( x ) = 0 for x = −2 pi , − pi , 0 , pi , 2 pi x = −2 pi , − pi , 0 , pi , 2 pi ⓔ ( −2 pi , 0 ) , ( − pi , 0 ) , ( −2 pi , 0 ) , ( − pi , 0 ) , ( 0 , 0 ) , ( pi , 0 ) , ( 2 pi , 0 ) ( 0 , 0 ) , ( pi , 0 ) , ( 2 pi , 0 ) ( f ) ( 0 , 0 ) ( f ) ( 0 , 0 ) ⓖ [ −2 pi , 2 pi ] [ −2 pi , 2 pi ] ⓗ [ −1 , 1 ] [ −1 , 1 ]

ⓐ f ( 0 ) = −6 f ( 0 ) = −6 ⓑ f ( −3 ) = 3 f ( −3 ) = 3 ⓒ f ( 3 ) = 3 f ( 3 ) = 3 ⓓ f ( x ) = 0 f ( x ) = 0 for no x ⓔ none ⓕ y = 6 y = 6 ⓖ [ −3 , 3 ] [ −3 , 3 ] ⓗ [ −3 , 6 ] [ −3 , 6 ]

( 0 , 3 ) ( 3 , 0 ) ( 0 , 3 ) ( 3 , 0 )

( 6 , 0 ) , ( 0 , 3 ) ( 6 , 0 ) , ( 0 , 3 )

( 16 , 0 ) , ( 0 , −12 ) ( 16 , 0 ) , ( 0 , −12 )

− 1 2 − 1 2

m = 5 3 ; ( 0 , −6 ) m = 5 3 ; ( 0 , −6 )

m = 4 5 ; ( 0 , − 8 5 ) m = 4 5 ; ( 0 , − 8 5 )

horizontal line

plotting points

ⓐ − $ 250 − $ 250 ⓑ $450 ⓒ The slope, 35, means that Marjorie’s weekly profit, P , increases by $35 for each additional student lesson she teaches. The P -intercept means that when the number of lessons is 0, Marjorie loses $250. ⓓ

not parallel

y = −5 x − 3 y = −5 x − 3

y = −2 x y = −2 x

y = −3 x + 5 y = −3 x + 5

y = 3 5 x y = 3 5 x

y = −2 x − 5 y = −2 x − 5

y = 1 2 x − 5 2 y = 1 2 x − 5 2

y = 2 y = 2

y = − 2 5 x + 8 y = − 2 5 x + 8

y = 3 y = 3

y = − 3 2 x − 6 y = − 3 2 x − 6

y = 1 y = 1

ⓐ yes ⓑ no ⓒ yes ⓓ yes; ⓔ no

y > 2 3 x − 3 y > 2 3 x − 3

x − 2 y ≥ 6 x − 2 y ≥ 6

ⓐ 20 x + 15 y ≥ 600 20 x + 15 y ≥ 600 ⓑ

ⓐ D: {−3, −2, −1, 0} ⓑ R: {7, 3, 9, −3, 8}

ⓐ (4, 3), (−2, −3), (−2, −1), (−3, 1), (0, −1), (0, 4), ⓑ D: {−3, −2, 0, 4} ⓒ R: {−3, −1, 1, 3, 4}

ⓐ yes ⓑ {−3, −2, −1, 0, 1, 2, 3} ⓒ {0, 1, 8, 27}

ⓐ {−3, −2, −1, 0, 1, 2, 3} ⓑ {−3, −2, −1, 0, 1, 2, 3} ⓒ {−243, −32, −1, 0, 1, 32, 243}

ⓐ f ( −2 ) = −10 f ( −2 ) = −10 ⓑ f ( 3 ) = 5 f ( 3 ) = 5 ⓒ f ( a ) = 3 a − 4 f ( a ) = 3 a − 4

ⓐ f ( −2 ) = 20 f ( −2 ) = 20 ⓑ f ( 3 ) = 0 f ( 3 ) = 0 ⓒ f ( a ) = a 2 − 5 a + 6 f ( a ) = a 2 − 5 a + 6

ⓑ D: (-∞,∞), R: (-∞,∞)

ⓑ D: (-∞,∞), R: (-∞,0]

ⓑ D: [ −2 , −2 , ∞), R: [0,∞)

ⓑ D: (-∞,∞), R: [1,∞)

D: (-∞,∞), R: [2,∞)

ⓐ f ( x ) = 0 f ( x ) = 0 ⓑ f ( π / 2 ) = 1 f ( π / 2 ) = 1 ⓒ f ( −3 π / 2 ) = 1 f ( −3 π / 2 ) = 1 ⓓ f ( x ) = 0 f ( x ) = 0 for x = −2 π , − π , 0 , π , 2 π x = −2 π , − π , 0 , π , 2 π ⓔ ( −2 π , 0 ) , ( −2 π , 0 ) , ( − π , 0 ) , ( − π , 0 ) , ( 0 , 0 ) , ( 0 , 0 ) , ( π , 0 ) , ( π , 0 ) , ( 2 π , 0 ) ( 2 π , 0 ) ( f ) ( 0 , 0 ) ( f ) ( 0 , 0 ) ⓖ [ −2 π , 2 π ] [ −2 π , 2 π ] ⓗ [ −1 , 1 ] [ −1 , 1 ]

ⓐ − 3 5 − 3 5 ⓑ undefined

y = − 4 5 x − 5 y = − 4 5 x − 5

ⓐ yes ⓑ { −3 , −2 , −1 , 0 , 1 , 2 , 3 } { −3 , −2 , −1 , 0 , 1 , 2 , 3 } ⓒ {0, 1, 8, 27}

ⓐ x = −2 , 2 x = −2 , 2 ⓑ y = −4 y = −4 ⓒ f ( −1 ) = −3 f ( −1 ) = −3 ⓓ f ( 1 ) = −3 f ( 1 ) = −3 ⓔ D: (-∞,∞) ⓕ R: [ −4 , −4 , ∞)

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• Authors: Lynn Marecek
• Publisher/website: OpenStax
• Book title: Intermediate Algebra
• Publication date: Mar 14, 2017
• Location: Houston, Texas
• Book URL: https://openstax.org/books/intermediate-algebra/pages/1-introduction
• Section URL: https://openstax.org/books/intermediate-algebra/pages/chapter-3

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