Graph the polynomial function. x ± ± 2 4 8 · Pre-Calc Final Pretest Multiple Choice Identify the choice that best completes the statement or answers the question. Describe the

Pre-Calc Final Pretest

Multiple Choice

Identify the choice that best completes the statement or answers the question.

Describe the end behavior of the graph of the function.

____ 1.

a. as and as

b. as and as

c. as and as

d. as and as

Graph the polynomial function.

____ 2.

a.

2 4–2–4 x

4

8

–4

–8

y

c.

2 4–2–4 x

4

8

–4

–8

y

b.

2 4–2–4 x

4

8

–4

–8

y

d.

2 4–2–4 x

4

8

–4

–8

y

Sketch a graph of the polynomial function f having the given characteristics. Use the graph to describe

the degree and leading coefficient of the function f.

____ 3. f is increasing when ; f is decreasing when .

when and ; when .

a. The degree is odd and the leading

coefficient is positive.

2 4 6–2–4–6 x

4

8

12

–4

–8

–12

y

c. The degree is even and the leading

coefficient is negative.

2 4 6–2–4–6 x

4

8

12

–4

–8

–12

y

b. The degree is even and the leading

coefficient is positive.

2 4 6–2–4–6 x

4

8

12

–4

–8

–12

y

d. The degree is odd and the leading

coefficient is negative.

2 4 6–2–4–6 x

4

8

12

–4

–8

–12

y

Find the difference.

____ 4.

a. c. b. d.

Find the product.

____ 5.

a. c. b. d.

____ 6.

a.

b. c. d.

Evaluate the expression without using a calculator.

____ 7.

a. – c. –

b.

d. – 4

Evaluate the expression using a calculator. Round your answer to two decimal places when

appropriate.

____ 8.

a. 0.14 c. 129.64

b. 3361.4 d. 7

Find the real solution(s) of the equation. Round your answer to two decimal places when appropriate.

____ 9.

a. c. b. d.

Use the properties of rational exponents to simplify the expression.

____ 10.

a. c. b. d.

Write the expression in simplest form.

____ 11.

a.

c.

b.

d.

Solve the equation. Check your solution(s).

____ 12.

a. c. b. d.

____ 13.

a. c. b. d.

Determine whether the inverse of f is a function. Then find the inverse.

____ 14.

a. no; c. yes; , where

b. no; , where d. yes;

____ 15.

a. yes, c. no,

b. no, d. yes,

____ 16. Which exponential function is shown in the graph below?

2 4 6–2–4–6 x

2

4

6

8

10

y

a. c.

b. d.

Evaluate the logarithm.

____ 17.

a. 0.01 c. 1

100

b. 2 d. –2

____ 18.

a. –3 c. 9

b. 1

3

d. 3

____ 19. Simplify .

a. e c. e

b. 1 d. 14

Find the inverse of the function.

____ 20.

a.

c.

b. d.

____ 21. Use and to evaluate .

a. 1.54 c. 0.589

b. 0.827 d. 1.654

Condense the logarithmic expression.

____ 22.

a. c.

b.

d.

____ 23. The amount of time T (in years) it will take for a population of a certain species to grow from 1550 to a can

be modeled by the function . Which function is equivalent?

a.

c.

b.

d.

Solve the equation.

____ 24.

a. x = –6 c. x = 4

b. x = 2 d. x = –12

Find the quotient.

____ 25.

a. , x

7

12, x 0

c.

b. , x

7

12

d. , x

7

12

____ 26. Draw an angle that measures –340° in standard position.

a. c.

b. d.

____ 27. Which angle is coterminal with 153°?

a. –27° c. –117°

b. 63° d. 513°

____ 28. Which angle is coterminal with 112°?

a. 382° c. 832°

b. –338° d. –68°

____ 29. Which angle is coterminal with –186°?

a. –456° c. –546°

b. –96° d. –366°

____ 30. Graph .

a.

2 3 4 5 6 7 x

1

2

3

4

5

6

–1

–2

–3

–4

y

c.

2 3 4 5 6 7 x

1

2

3

4

5

6

–1

–2

–3

–4

y

b.

2 3 4 5 6 7 x

1

2

3

4

5

6

–1

–2

–3

–4

y

d.

2 3 4 5 6 7 x

1

2

3

4

5

6

–1

–2

–3

–4

y

____ 31. Choose the correct function for the sinusoid shown.

( 0 , 0 )

(—8 , –6)

—4

—2

x

1

2

3

–1

–2

–3

–4

–5

–6

–7

–8

–9

y

a. c.

b. d.

Multiple Response

Identify one or more choices that best complete the statement or answer the question.

____ 1. Which polynomials have been factored correctly?

a.

d.

b.

e.

c.

f.

____ 2. Which statements are true about the polynomial function ?

a. The graph of f is shown below.

1 2 3 4–1–2–3–4 x

2

4

6

8

–2

–4

–6

–8

y

b.

c. The function has a local minimum at .

d. The function is odd.

e. The function has a local maximum at .

____ 3. Which statements about the data are true?

x –3 –2 –1 0 1 2 3

f(x) –14 –6 0 4 6 6 4

a. A polynomial function that fits the data exactly is

b. A polynomial function that fits the data exactly is

c. The third finite differences are constant and equal –28.

d. A polynomial function that fits the data exactly is .

e. The second finite differences are constant and equal –2.

f. The first finite differences are constant and equal 8.

____ 4. Which of the following are true about the function g graphed below?

2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

a.

b. of the graph of

.

c. of the graph of

.

d. ,

e. ,

f.

____ 5. Which equations are correct?

a.

b.

c.

d.

e.

____ 6. Choose the correct trigonometric functions of the angle .

12

13

a. sec

13

5

d. csc

13

12

b. cos

5

13

e. tan

5

12

c. sin

12

13

f. cot

12

5

____ 7. Choose the function(s) represented by the graph.

( —10

, 5 )

(3—10

,–5)

—4

—2

3—4

x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

a. y =

c. y =

b. y = d. y =

____ 8. Select all true statements of the graph below.

—5

2—5

3—5

-—5

-2—5

-3—5

x

1

2

–1

–2

y

a. The function of the graph is .

b. The period of the graph is .

c. The function of the graph is .

d. represents a vertical shrink of the graph by a factor of

1

8.

Numeric Response

Identify the number of solutions or zeros.

1.

Evaluate the expression without using a calculator.

2.

3.

4.

Evaluate the expression using a calculator. Round your answer to two decimal places when

appropriate.

5.

6.

Find the real solution(s) of the equation. Round your answer to two decimal places when appropriate.

7.

8. An investor deposits $9000 into an account that earns simple interest at 5.45% annually. The amount A (in

dollars) in the account is calculated using the formula

In the formula, P is the principal (in dollars), r is the interest rate (in decimal form), and t is the time (in

years). How much interest is gained on the investment after 3 months?

Newton’s Law of Cooling states that for a cooling substance with initial temperature , the

temperature T after t minutes can be modeled by , where is the surrounding

temperature and r is the cooling rate of the substance.

9. How long it will take for a 112°F cup of coffee to cool to a temperature of 85°F when the surrounding

temperature is 56°F and the cooling rate of coffee is 0.034? Round your answer to the nearest minute.

10. Find the value of x for the right triangle. Round your answer to the nearest hundredth.

45°

19x

Matching

Match the function below with its zeros.

a. 0,

1

4, and

7

4

d. –8, –5, and

4

5

b. 0, 3, and 1 e. , and

c. f. 0, 4, and 18

____ 1.

____ 2.

____ 3.

Match the equivalent equations.

a. e.

b. f. c.

g.

d.

h.

____ 4.

____ 5.

____ 6.

____ 7.

____ 8.

Match the function below to its graph.

a.

2 3 4 5 6 7 8-

x

2

4

6

–2

–4

–6

y

d.

—2

3 —

2

5 —

2

x

0.5

1

1.5

–0.5

–1

–1.5

y

b.

—2

3—2

2 5—2

x

1

2

3

4

–1

–2

–3

–4

y

e.

—2

3—2

2 5—2

x

1

2

3

4

–1

–2

–3

–4

y

c.

2 3 4 5 6

7 8

- x

1

–1

y

f.

—2

3—2

5 —

2

x

1

–1

y

____ 9.

____ 10.

____ 11.

____ 12.

Pre-Calc Final Pretest

Answer Section

MULTIPLE CHOICE

1. ANS: D PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.1

NAT: HSF-IF.B.4 KEY: end behavior | polynomial function | polynomial

NOT: Example 3


NAT: HSF-IF.B.4 | HSF-IF.C.7c

KEY: graphing polynomial functions | polynomial function | polynomial | graph of a polynomial function |

sketching graphs of polynomial functions NOT: Example 4

3. ANS: B PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 4.1

NAT: HSF-IF.B.4 | HSF-IF.C.7c

KEY: sketching graphs of polynomial functions | polynomial function | polynomial | graph of a polynomial

function NOT: Example 5

4. ANS: A PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.2

NAT: HSA-APR.A.1 KEY: subtracting polynomials | polynomial

NOT: Example 2


NAT: HSA-APR.A.1 | HSA-APR.C.4 KEY: multiplying polynomials | polynomial

NOT: Example 3


NAT: HSA-APR.A.1 | HSA-APR.C.4 KEY: multiplying polynomials | polynomial

NOT: Example 3


NAT: HSN-RN.A.1 | HSN-RN.A.2 KEY: evaluating expressions with rational exponents

NOT: Example 2


NAT: HSN-RN.A.1 | HSN-RN.A.2 KEY: approximating expressions with rational exponents

NOT: Example 3

9. ANS: C PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 5.1

NAT: HSN-RN.A.1 | HSN-RN.A.2 KEY: solving equations using nth roots

NOT: Example 4


NAT: HSN-RN.A.2

KEY: properties of rational exponents | simplifying expressions with rational exponents

NOT: Example 1


NAT: HSN-RN.A.2 KEY: writing radical expressions in simplest form

NOT: Example 4


NAT: HSA-REI.A.1 | HSA-REI.A.2 KEY: radical equation | solving radical equations

NOT: Example 1


NAT: HSA-REI.A.1 | HSA-REI.A.2 KEY: radical equation | solving radical equations

NOT: Example 1


NAT: HSA-CED.A.4 | HSF-BF.B.4a KEY: inverse functions | finding inverses of nonlinear functions

NOT: Example 5


NAT: HSA-CED.A.4 | HSF-BF.B.4a KEY: inverse functions | finding inverses of nonlinear functions

NOT: Example 5


NAT: HSF-IF.C.7e

KEY: natural base exponential function | graphing natural base exponential functions | graph of an

exponential function NOT: Example 2


NAT: HSF-LE.A.4 KEY: evaluating logarithms | logarithmic expression

NOT: Example 3


NAT: HSF-LE.A.4 KEY: evaluating logarithms | logarithmic expression

NOT: Example 3


NAT: HSF-BF.B.4a | HSF-LE.A.4

KEY: using inverse properties of logarithmic and exponential functions | simplifying logarithmic expressions

NOT: Example 5


NAT: HSF-BF.B.4a | HSF-LE.A.4 KEY: inverse functions | finding inverse functions

NOT: Example 6


NAT: HSA-SSE.A.2 KEY: properties of logarithms | evaluating logarithms

NOT: Example 1


NAT: HSA-SSE.A.2

KEY: properties of logarithms | condensing logarithmic expressions

NOT: Example 3


NAT: HSA-SSE.A.2 | HSF-LE.A.4 KEY: application | logarithmic function

NOT: Example 6-1


NAT: HSA-REI.A.1 | HSF-LE.A.4 KEY: logarithmic equations | solving logarithmic equations

NOT: Example 3


NAT: HSA-APR.D.6 | HSA-APR.D.7 KEY: dividing rational expressions | rational expression

NOT: Example 6


NAT: HSF-TF.A.1 KEY: drawing angles in standard position | standard position | measure of an angle

NOT: Example 1


NAT: HSF-TF.A.1 KEY: coterminal | finding coterminal angles | coterminal angles

NOT: Example 2



NOT: Example 2



NOT: Example 2


NAT: HSF-IF.C.7e | HSF-BF.B.3 KEY: graph of a periodic function | periodic function

NOT: Example 3


NAT: HSF-TF.B.5 | HSF-BF.A.1a | HSA-CED.A.2

KEY: writing trigonometric functions | writing sinusoidal models | graph of a periodic function

NOT: Example 2

MULTIPLE RESPONSE

1. ANS: A, B, C, D PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 4.4

NAT: HSA-SSE.A.2 | HSA-APR.B.2 | HSA-APR.B.3

KEY: factoring polynomials | factored completely | polynomial | quadratic form

NOT: Combined Concept

2. ANS: B, E PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 4.8

NAT: HSA-APR.B.3 | HSF-IF.B.4 | HSF-IF.C.7c | HSF-BF.B.3

KEY: finding real zeros of polynomial functions | graph of a polynomial function | turning points |

x-intercepts | increasing | decreasing | local maximum | local minimum | graphing polynomial functions |

graph of a polynomial function | sketching graphs of polynomial functions | even function | odd function


3. ANS: D, E PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 4.9

NAT: HSA-CED.A.2 | HSF-BF.A.1a

KEY: writing polynomial functions for sets of points | writing polynomial functions | graph of a polynomial

function | polynomial function | writing polynomial functions using finite differences | finite differences |

modeling data | technology NOT: Combined Concept

4. ANS: A, B, D PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 5.3

NAT: HSF-IF.C.7b | HSF-BF.B.3

KEY: radical function | graphing radical functions | transformations of radical functions | writing

transformations of radical functions NOT: Combined Concept

5. ANS: C, D, E PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 6.5

NAT: HSA-SSE.A.2 | HSF-LE.A.4

KEY: change-of-base formula | evaluating logarithms | logarithmic function | expanding logarithmic

functions | condensing logarithmic functions | properties of logarithms


6. ANS: A, B, C, D PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 9.1

NAT: HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8

KEY: evaluating trigonometric functions of acute angles | sine |cosine | tangent | cosecant | secant | cotangent

NOT: Example 1

7. ANS: B, D PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 9.6

NAT: HSF-TF.B.5 | HSF-BF.A.1a | HSA-CED.A.2

KEY: trigonometric function | writing sinusoidal models | graph of a periodic function


8. ANS: A, B, D PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 9.5

NAT: HSF-IF.C.7e | HSF-BF.B.3

KEY: secant function | cosecant function | graph of a periodic function | graphing secant functions | graphing

cosecant functions | tangent function | graphing tangent functions | cotangent function | graphing cotangent

functions | sine function | graphing sine functions | cosine function | graphing cosine functions

NOT: Application-2

NUMERIC RESPONSE

1. ANS: 4

PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.6

NAT: HSN-CN.C.9 | HSA-APR.B.3 KEY: finding the number of solutions or zeros

NOT: Example 1

2. ANS: 5



NOT: Example 2

3. ANS: 128



NOT: Example 2

4. ANS: –8



NOT: Example 2

5. ANS: 13.09



NOT: Example 3

6. ANS: 38.4



NOT: Example 3

7. ANS: 5


NAT: HSN-RN.A.1 | HSN-RN.A.2 KEY: solving equations using nth roots

NOT: Example 4

8. ANS: $120.20


NAT: HSN-RN.A.1 | HSN-RN.A.2

KEY: application | evaluating expressions with rational exponents

NOT: Example 5-2

9. ANS: 19


NAT: HSA-REI.A.1 | HSF-LE.A.4 KEY: application | exponential equations

NOT: Example 2-1

10. ANS: 13.44


NAT: HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8

KEY: cosine | trigonometric function | right triangle | unknown side length

NOT: Example 3

MATCHING

1. ANS: F PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 4.5

NAT: HSA-APR.B.3

KEY: finding zeros of polynomial functions | polynomial function | zero of a function



NAT: HSA-APR.B.3




NAT: HSA-APR.B.3





KEY: evaluating expressions with rational exponents | finding nth roots










7. ANS: H PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 5.1




8. ANS: E PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 5.1






KEY: graphing sine functions | sine function | graph of a periodic function | graphing cosine functions |

cosine function NOT: Combined Concept





11. ANS: E PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 9.4








Documents

Graph the polynomial function. x ± ± 2 4 8 · Pre-Calc Final Pretest Multiple Choice Identify the choice that best completes the statement or answers the question. Describe the