Chapter 5 test Review Integrated 1

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1 Name: Class: _ Date: _ ID: A Chapter 5 test Review Integrated 1 Find the balance in the account. 1. $700 principal earning 2.25%, compounded quarterly, after 6 years a. $72.96 c. $ b. $ d. $17, The function S(x) = 2 x 1 models the number of digital songs James has downloaded after x weeks. According to the model, after how many weeks will he have downloaded 2 songs? a. 4 weeks c. 17 weeks b. 15 weeks d. 6 weeks. f(x) = 5 4 x and g(x) = 4 x + 2. What is (f g)(x) and (f g)()? a. (f g)(x) = 5 4 x + 2; (f g)() = 22 b. (f g)(x) = 4 4 x + 2; (f g)() = 258 c. (f g)(x) = 5 4 x 2; (f g)() = 18 d. (f g)(x) = 4 4 x 2; (f g)() = f(x) = x 8 and g(x) = 9x +. What are (f + g)(x) and (f + g)( 5)? a. (f + g)(x) = 6x 5; (f + g)( 5) = 5 c. (f + g)(x) = 6x + 5; (f + g)( 5) = 25 b. (f + g)(x) = 6x + 5; (f + g)( 5) = 5 d. (f + g)(x) = 6x 5; (f + g)( 5) = Is the sequence geometric? If so, identify the common ratio. 2, 4, 16, 6,... a. yes; 2 b. yes; 2 c. yes; d. no 6. Does the table represent a linear or an exponential function? x y a. linear b. exponential 7. Suppose an investment of $,800 doubles in value every decade. The function f(x) =,800 2 x gives the value of the investment after x decades. How much is the investment worth after 2 decades? a. $15,200 c. $15,200 b. $152,000 d. $76,000 1

2 Name: ID: A 8. Which is the piecewise definition for the absolute value function f(x) = x 1? x + 1, for x 1 a. f(x) = Ì x 1, for x 1 c. f(x) = Ì Ó x 1, for x < 1 Ó x + 1, for x < 1 x + 1, for x 1 b. f(x) = Ì x 1, for x 1 d. f(x) = Ì Ó x + 1, for x < 1 Ó x + 1, for x < 1 9. Which graph represents the function f(x) = x + 2? a. c. b. d. 10. Suppose the population of a town is 8,600 and is growing % each year. Predict the population after years. a. about 22,200 people b. about 77,400 people c. about 9,97 people d. about people 2

3 Name: ID: A 11. What is the average rate of change for the function f(x) = 6x + 1 over the interval 0 x 7? a. 1 c. 6 1 b. 6 d What is the value of 4x y for x = and y = 1? a. 4 ( ) 0 b. 4 c. 108 d Simplify the radical expression. a. 16 b. 10 c d x 15 y 9 7xy 11 a. 9x 7 y b. 9x 7 y c. x 7 y d. 8x 7 y 4 7xy 11 xy h 6 k 4 a. 2h k 2 5 c. hk 10 b. 2 5h 6 k 4 d. 4 5h 6 k 4

4 Name: ID: A 16. Which is the cube root function graphed below? a. g(x) = x b. g(x) = c. g(x) = x x d. g(x) = 2 x 2 Ê f ˆ 17. f(x) = 154x 44 and g(x) = 22. What are g ËÁ f and (x) Ê ËÁ g ˆ (5)? a. 7x 2; c. 7x + 2; 7 b. 12x + 22; 682 d. 12x 22; 68 Simplify the radical expression by rationalizing the denominator a. 11 b c. 11 d Solve the exponential equation. 19. x + 5 = 1 81 a. x = 5 4 b. x = 1 9 c. x = 9 d. x = 1 4

5 Name: ID: A 20. What is the piecewise function graphed below? 2x + 2, for x > 2 a. f(x) = Ì Ó x + 6, for x 2 2x + 6, for x > 2 b. f(x) = Ì Ó x + 4, for x 2 2x + 2, for x 2 c. f(x) = Ì Ó x + 6, for x < 2 2x + 6, for x 2 d. f(x) = Ì Ó x + 4, for x < 2 What is the simplified form of each expression? 21. ( 4.2) 0 a. 1 b. 4.2 c. 1 d a 5 a. 5a b. a 5 c. a 5 d. 5 a 2. Which situation is NOT modeled using an exponential function? a. Karl spends $40 on gas each week to drive to work. b. A company s sales are expected to double each year. c. The number of people playing a video game increases by 0% each month. d. The amount Diane owes on her car loan decreases by 10% every three months. 5

6 Name: ID: A 24. What is an exponential function that represents the table? x y a. y = 18 x c. y = x b. y = 18 x d. Ê 1 ˆ y = 18 ËÁ 25. Graph the function g(x) = x Then identify the domain and range of the function. x 6

7 ID: A Chapter 5 test Review Integrated 1 Answer Section 1. ANS: C PTS: 1 DIF: L REF: 5-4 Exponential Growth and Decay OBJ: To model exponential growth and decay NAT: CC A.SSE.1.b CC A.SSE..c CC A.CED.2 CC F.IF.4 CC F.IF.8.b CC F.BF. CC F.LE.1.c CC F.LE.5 A.2.g A..h A.4.c TOP: 5-4 Problem 2 Compound Interest KEY: exponential growth growth factor compound interest 2. ANS: D PTS: 1 DIF: L REF: 5-5 Solving Exponential Equations OBJ: To solve exponential equations NAT: CC A.CED.1 CC A.REI.11 TOP: 5-5 Problem 2 Solving Real-World Exponential Equations. ANS: D PTS: 1 DIF: L2 REF: 5-7 Combining Functions OBJ: To add, subtract, multiply, and divide linear and exponential functions NAT: CC F.BF.1.b TOP: 5-7 Problem 1 Adding and Subtracting Functions 4. ANS: D PTS: 1 DIF: L2 REF: 5-7 Combining Functions OBJ: To add, subtract, multiply, and divide linear and exponential functions NAT: CC F.BF.1.b TOP: 5-7 Problem 1 Adding and Subtracting Functions 5. ANS: D PTS: 1 DIF: L REF: 5-6 Geometric Sequences OBJ: To write and use recursive formulas for geometric sequences NAT: CC A.SSE.1.a CC F.IF. CC F.BF.1.a CC F.BF.2 CC F.LE.2 TOP: 5-6 Problem 1 Identifying Geometric Sequences KEY: geometric sequence common ratio 6. ANS: A PTS: 1 DIF: L2 REF: 5- Comparing Linear and Exponential Functions OBJ: 5-.1 To compare properties of linear and exponential functions NAT: CC F.IF.6 CC F.IF.7 CC F.IF.9 CC F.LE.1 CC F.LE.1.a CC F.LE. TOP: 5- Problem 1 Identifying Linear and Exponential Functions 7. ANS: C PTS: 1 DIF: L REF: 5-2 Exponential Functions OBJ: To evaluate and graph exponential functions NAT: CC A.CED.2 CC A.REI.11 CC F.IF.4 CC F.IF.5 CC F.IF.7.e CC F.IF.9 CC F.LE.2 A.1.b A.1.e A.1.h A.2.h A..h TOP: 5-2 Problem 1 Evaluating an Exponential Function KEY: exponential function 8. ANS: C PTS: 1 DIF: L REF: 5-9 Radical and Piecewise Functions OBJ: To understand properties of radical and piecewise functions NAT: CC F.IF.4 CC F.IF.5 CC F.IF.6 CC F.IF.9 TOP: 5-9 Problem 4 Writing a Piecewise Function KEY: piecewise function DOK: 2 1

8 ID: A 9. ANS: C PTS: 1 DIF: L2 REF: 5-9 Radical and Piecewise Functions OBJ: To understand properties of radical and piecewise functions NAT: CC F.IF.4 CC F.IF.5 CC F.IF.6 CC F.IF.9 TOP: 5-9 Problem 1 Graphing a Square Root Function KEY: square root function DOK: ANS: C PTS: 1 DIF: L4 REF: 5-4 Exponential Growth and Decay OBJ: To model exponential growth and decay NAT: CC A.SSE.1.b CC A.SSE..c CC A.CED.2 CC F.IF.4 CC F.IF.8.b CC F.BF. CC F.LE.1.c CC F.LE.5 A.2.g A..h A.4.c TOP: 5-4 Problem 1 Modeling Exponential Growth KEY: exponential growth growth factor 11. ANS: B PTS: 1 DIF: L2 REF: 5- Comparing Linear and Exponential Functions OBJ: 5-.1 To compare properties of linear and exponential functions NAT: CC F.IF.6 CC F.IF.7 CC F.IF.9 CC F.LE.1 CC F.LE.1.a CC F.LE. TOP: 5- Problem Investigating Rates of Change KEY: average rate of change DOK: ANS: B PTS: 1 DIF: L2 REF: 5-1 Zero and Negative Exponents OBJ: To simplify expressions involving zero and negative exponents NAT: CC N.RN.1 CC N.RN.2 N.1.d N..a A..c A..h TOP: 5-1 Problem Evaluating an Exponential Expression KEY: evaluating expressions negative exponents 1. ANS: D PTS: 1 DIF: L2 REF: 10-2 Simplifying Radicals OBJ: To simplify radicals involving products and quotients NAT: CC A.REI.2 A..e TOP: 5-8 Problem 1 Removing Perfect-Square Factors KEY: radical expression 14. ANS: C PTS: 1 DIF: L4 REF: 10-2 Simplifying Radicals OBJ: To simplify radicals involving products and quotients NAT: CC A.REI.2 A..e TOP: 5-8 Problem 5 Simplifying Fractions Within Radicals KEY: radical expression 15. ANS: A PTS: 1 DIF: L4 REF: 10-2 Simplifying Radicals OBJ: To simplify radicals involving products and quotients NAT: CC A.REI.2 A..e TOP: 5-8 Problem 2 Removing Variable Factors KEY: radical expression 16. ANS: A PTS: 1 DIF: L2 REF: 5-9 Radical and Piecewise Functions OBJ: To understand properties of radical and piecewise functions NAT: CC F.IF.4 CC F.IF.5 CC F.IF.6 CC F.IF.9 TOP: 5-9 Problem 2 Graphing a Cube Root Function KEY: cube root function DOK: ANS: A PTS: 1 DIF: L1 REF: 5-7 Combining Functions OBJ: To add, subtract, multiply, and divide linear and exponential functions NAT: CC F.BF.1.b TOP: 5-7 Problem 2 Multiplying and Dividing Functions 2

9 ID: A 18. ANS: B PTS: 1 DIF: L2 REF: 10-2 Simplifying Radicals OBJ: To simplify radicals involving products and quotients NAT: CC A.REI.2 A..e TOP: 5-8 Problem 6 Rationalizing Denominators KEY: radical expression rationalize the denominator 19. ANS: C PTS: 1 DIF: L REF: 5-5 Solving Exponential Equations OBJ: To solve exponential equations NAT: CC A.CED.1 CC A.REI.11 TOP: 5-5 Problem 1 Solving Exponential Equations With the Same Base 20. ANS: B PTS: 1 DIF: L REF: 5-9 Radical and Piecewise Functions OBJ: To understand properties of radical and piecewise functions NAT: CC F.IF.4 CC F.IF.5 CC F.IF.6 CC F.IF.9 TOP: 5-9 Problem Graphing a Piecewise Function KEY: piecewise function DOK: ANS: C PTS: 1 DIF: L2 REF: 5-1 Zero and Negative Exponents OBJ: To simplify expressions involving zero and negative exponents NAT: CC N.RN.1 CC N.RN.2 N.1.d N..a A..c A..h TOP: 5-1 Problem 1 Simplifying Powers KEY: simplify expressions zero exponents 22. ANS: C PTS: 1 DIF: L REF: 5-1 Zero and Negative Exponents OBJ: To simplify expressions involving zero and negative exponents NAT: CC N.RN.1 CC N.RN.2 N.1.d N..a A..c A..h TOP: 5-1 Problem 2 Simplifying Exponential Expressions KEY: simplify expressions zero exponents negative exponents 2. ANS: A PTS: 1 DIF: L REF: 5- Comparing Linear and Exponential Functions OBJ: 5-.1 To compare properties of linear and exponential functions NAT: CC F.IF.6 CC F.IF.7 CC F.IF.9 CC F.LE.1 CC F.LE.1.a CC F.LE. TOP: 5- Problem 2 Identifying Real-World Linear and Exponential Functions 24. ANS: B PTS: 1 DIF: L REF: 5-4 Exponential Growth and Decay OBJ: To model exponential growth and decay NAT: CC A.SSE.1.a CC A.SSE.1.b CC A.CED.2 CC F.IF.4 CC F.IF.7 CC F.BF.1.a CC F.LE.1.c CC F.LE.2 CC F.LE.5 TOP: 5-4 Problem 4 Writing Exponential Functions

10 ID: A 25. ANS: domain: x ; range: y 4 PTS: 1 DIF: L REF: 5-9 Radical and Piecewise Functions OBJ: To understand properties of radical and piecewise functions NAT: CC F.IF.4 CC F.IF.5 CC F.IF.6 CC F.IF.9 TOP: 5-9 Problem 1 Graphing a Square Root Function KEY: square root function DOK: 2 4

Name: Class: Date: a. Use inequality statements to write the domain and range of f(x).

Name: Class: Date: a. Use inequality statements to write the domain and range of f(x). Name: Class: Date: ID: A Chapter 9 Review 1. The graph of the square root function, f(), is shown. a. Use inequality statements to write the domain and range of f(). b. Sketch the graph obtained by shifting