Unit 5: Radical Functions & Rational Exponents

Version A

Multiple Choice Identify the letter of the choice that best completes the statement or answers the question.

____ 1. Find all the real square roots of 0.0004.

a. 0.00632 and –0.00632 c. 0.0002 and –0.0002

b. 0.06325 and –0.06325 d. 0.02 and –0.02

Find the real-number root.

____ 2.

a. –1.6 c. –1.28

b. 1.6 d. no real number root

____ 3.

a. b. c. d.

Simplify the radical expression. Use absolute value symbols if needed.

____ 4.

a. b. c. d.

Multiply and simplify if possible.

____ 5.

a. b. c. d. not possible Version A

____ 6. Multiply and simplify . Assume that all variables are positive.

b. d. none of these

____ 7.

a. b. c. d.

Rationalize the denominator of the expression. Assume that all variables are positive.

____ 8.

Add if possible.

____ 9.

b. d. not possible to simplify

Subtract if possible.

____ 10.

b. d. not possible to simplify Version A

____ 11. A garden has width and length . What is the perimeter of the garden in simplest radical form?

a. units c. 91 units

b. units d. units

Simplify.

____ 12.

a. b. c. 20 d. 1

____ 13. a. 512 b. 4,096 c. 16 d.

Multiply.

____ 14.

____ 15. Write the exponential expression in radical form.

a. b. c. d.

____ 16. Write in simplest form.

b. d. none of these Version A

Solve the equation.

____ 17.

a. 14 b. –8 c. 4 d. –6

____ 18.

a. 11 b. 15; –1 c. –3 d. 1; –1

____ 19. Let and . Find .

a. 23 b. –53 c. –9 d. 3

____ 20. Find the inverse of .

b. d. Version A

Graph the function.

____ 21.

a. y c. y

–4 –2 2 4 x –4 –2 2 4 x –2 –2

–4 –4

b. y d. y

–4 –2 2 4 x –4 –2 2 4 x –2 –2

–4 –4 Version A

____ 22.

a. y c. y

–4 –2 2 4 x –4 –2 2 4 x –2 –2

–4 –4

b. y d. y

–4 –2 2 4 x –4 –2 2 4 x –2 –2

–4 –4 Version A

Short Answer

23. The velocity of sound in air is given by the equation , where v is the velocity in meters per second and t is the temperature in degrees Celsius.

a. Find the temperature when the velocity of sound in air is 318 meters per second. Round the answer to the nearest degree.

b. Find the velocity of sound in meters per second when the temperature is 20°C. Round the answer to the nearest meter per second.

24. Let and .

a. Find f(g(x)).

b. Find g(f(x)).

25. The velocity of sound in air is given by the equation , where v is the velocity in meters per second and t is the temperature in degrees Celsius.

a. Graph the equation on your calculator. Make a sketch of the graph.

b. Find the temperature when the velocity is 329 meters per second. Round the answer to the nearest degree. Version A

Unit 5: Radical Functions & Rational Exponents Answer Section

MULTIPLE CHOICE

1. ANS: D DIF: L1 REF: 7-1 Roots and Radical Expressions OBJ: 7-1.1 Roots and Radical Expressions STO: MD 1.1.1, MD 2.3.2 TOP: 7-1 Example 1 KEY: square root,real roots MSC: NAEP N1d, NAEP N5f, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, TV.LV21/22.10, TV.LV21/22.11, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 2. ANS: D DIF: L1 REF: 7-1 Roots and Radical Expressions OBJ: 7-1.1 Roots and Radical Expressions STO: MD 1.1.1, MD 2.3.2 TOP: 7-1 Example 2 KEY: real roots MSC: NAEP N1d, NAEP N5f, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, TV.LV21/22.10, TV.LV21/22.11, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 3. ANS: D DIF: L2 REF: 7-1 Roots and Radical Expressions OBJ: 7-1.1 Roots and Radical Expressions STO: MD 1.1.1, MD 2.3.2 TOP: 7-1 Example 2 KEY: real roots MSC: NAEP N1d, NAEP N5f, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, TV.LV21/22.10, TV.LV21/22.11, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 4. ANS: A DIF: L2 REF: 7-1 Roots and Radical Expressions OBJ: 7-1.1 Roots and Radical Expressions STO: MD 1.1.1, MD 2.3.2 TOP: 7-1 Example 3 KEY: simplifying a radical expression MSC: NAEP N1d, NAEP N5f, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, TV.LV21/22.10, TV.LV21/22.11, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 5. ANS: A DIF: L1 REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.1 Multiplying Radical Expressions STO: MD 1.1.3 TOP: 7-2 Example 1 KEY: multiplying radical expressions,simplifying a radical expression MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, TV.LV21/22.12, TV.LV21/22.16, TV.LV21/22.52, TV.LVALG.53 6. ANS: A DIF: L1 REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.1 Multiplying Radical Expressions STO: MD 1.1.3 TOP: 7-2 Example 3 KEY: multiplying radical expressions,simplifying a radical expression MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, TV.LV21/22.12, TV.LV21/22.16, TV.LV21/22.52, TV.LVALG.53 7. ANS: B DIF: L2 REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.2 Dividing Radical Expressions STO: MD 1.1.3 TOP: 7-2 Example 4 KEY: simplifying a radical expression,divide radical expressions,rationalize the denominator MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, CAT5.LV21/22.52, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.11, Version A

TV.LV21/22.12, TV.LV21/22.16, TV.LV21/22.52, TV.LVALG.53 8. ANS: C DIF: L1 REF: 7-3 Binomial Radical Expressions OBJ: 7-3.2 Multiplying and Dividing Binomial Radical Expressions STO: MD 1.1.3 TOP: 7-3 Example 6 KEY: binomial radical expressions,conjugates,multiplying binomial radical expressions,simplifying a radical expression MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 9. ANS: C DIF: L1 REF: 7-3 Binomial Radical Expressions OBJ: 7-3.1 Adding and Subtracting Radical Expressions STO: MD 1.1.3 TOP: 7-3 Example 1 KEY: binomial radical expressions,adding radical expressions,like radicals MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 10. ANS: C DIF: L1 REF: 7-3 Binomial Radical Expressions OBJ: 7-3.1 Adding and Subtracting Radical Expressions STO: MD 1.1.3 TOP: 7-3 Example 1 KEY: binomial radical expressions,adding radical expressions,like radicals MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 11. ANS: B DIF: L1 REF: 7-3 Binomial Radical Expressions OBJ: 7-3.1 Adding and Subtracting Radical Expressions STO: MD 1.1.3 TOP: 7-3 Example 2 KEY: adding radical expressions,problem solving MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 12. ANS: C DIF: L1 REF: 7-4 Rational Exponents OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STO: MD 1.1.1, MD 1.1.2 TOP: 7-4 Example 1 KEY: rational exponent MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.10, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 13. ANS: C DIF: L1 REF: 7-4 Rational Exponents OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STO: MD 1.1.1, MD 1.1.2 TOP: 7-4 Example 4 KEY: rational exponent MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.10, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 14. ANS: B DIF: L1 REF: 7-3 Binomial Radical Expressions OBJ: 7-3.2 Multiplying and Dividing Binomial Radical Expressions STO: MD 1.1.3 TOP: 7-3 Example 4 KEY: binomial radical expressions,simplifying a radical expression,multiplying binomial radical expressions MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 15. ANS: A DIF: L1 REF: 7-4 Rational Exponents OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STO: MD 1.1.1, MD 1.1.2 TOP: 7-4 Example 2 KEY: rational exponent,radical form MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.10, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 16. ANS: A DIF: L1 REF: 7-4 Rational Exponents Version A

OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STO: MD 1.1.1, MD 1.1.2 TOP: 7-4 Example 5 KEY: rational exponent MSC: NAEP A3b, CAT5.LV21/22.50, CAT5.LV21/22.51, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.10, TV.LV21/22.12, TV.LV21/22.52, TV.LVALG.53 17. ANS: D DIF: L1 REF: 7-5 Solving Radical Equations OBJ: 7-5.1 Solving Radical Equations STO: MD 1.1.1 TOP: 7-5 Example 1 KEY: radical equation, MSC: NAEP A4a, CAT5.LV21/22.50, CAT5.LV21/22.55, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.GM, S9.TSK3.PRA, S10.TSK3.GM, S10.TSK3.PRA, TV.LV21/22.13, TV.LV21/22.52, TV.LVALG.53 18. ANS: B DIF: L1 REF: 7-5 Solving Radical Equations OBJ: 7-5.1 Solving Radical Equations STO: MD 1.1.1 TOP: 7-5 Example 2 KEY: radical equation,rational exponent MSC: NAEP A4a, CAT5.LV21/22.50, CAT5.LV21/22.55, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.GM, S9.TSK3.PRA, S10.TSK3.GM, S10.TSK3.PRA, TV.LV21/22.13, TV.LV21/22.52, TV.LVALG.53 19. ANS: B DIF: L1 REF: 7-6 Function Operations OBJ: 7-6.2 Composition of Functions STO: MD 1.1.3 TOP: 7-6 Example 3 KEY: composition of functions,operations with functions MSC: NAEP A1g, NAEP A3b, CAT5.LV21/22.49, CAT5.LV21/22.50, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.51, TV.LV21/22.52, TV.LVALG.56 20. ANS: A DIF: L1 REF: 7-7 Inverse Relations and Functions OBJ: 7-7.1 The Inverse of a Function STO: MD 1.1.2 TOP: 7-7 Example 2 KEY: inverse relations and functions, MSC: NAEP A2c, CAT5.LV21/22.50, CAT5.LV21/22.56, IT.LV17/18.AM, S9.TSK3.GM, S9.TSK3.PRA, S10.TSK3.GM, S10.TSK3.PRA, TV.LV21/22.14, TV.LV21/22.52, TV.LVALG.56 21. ANS: A DIF: L1 REF: 7-8 Graphing Radical Functions OBJ: 7-8.1 Radical Functions STO: MD 2.1.3 TOP: 7-8 Example 1 KEY: domain,graphing,range,radical function,translation MSC: NAEP A2a, CAT5.LV21/22.53, CAT5.LV21/22.56, IT.LV17/18.AM, S9.TSK3.DSP, S9.TSK3.GM, S10.TSK3.DSP, S10.TSK3.GM, TV.LV21/22.14, TV.LV21/22.15, TV.LVALG.56 22. ANS: C DIF: L1 REF: 7-8 Graphing Radical Functions OBJ: 7-8.1 Radical Functions STO: MD 2.1.3 TOP: 7-8 Example 2 KEY: domain,graphing,range,radical function,translation MSC: NAEP A2a, CAT5.LV21/22.53, CAT5.LV21/22.56, IT.LV17/18.AM, S9.TSK3.DSP, S9.TSK3.GM, S10.TSK3.DSP, S10.TSK3.GM, TV.LV21/22.14, TV.LV21/22.15, TV.LVALG.56

SHORT ANSWER

23. ANS: a. –20°C b. 342 meters per second

DIF: L2 REF: 7-5 Solving Radical Equations OBJ: 7-5.1 Solving Radical Equations STO: MD 1.1.1 TOP: 7-5 Example 1 KEY: radical equation,problem solving,multi-part question,word problem MSC: NAEP A4a, CAT5.LV21/22.50, CAT5.LV21/22.55, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.GM, S9.TSK3.PRA, S10.TSK3.GM, S10.TSK3.PRA, TV.LV21/22.13, TV.LV21/22.52, TV.LVALG.53 24. ANS: Version A

DIF: L2 REF: 7-6 Function Operations OBJ: 7-6.2 Composition of Functions STO: MD 1.1.3 TOP: 7-6 Example 3 KEY: composition of functions,multi-part question,operations with functions MSC: NAEP A1g, NAEP A3b, CAT5.LV21/22.49, CAT5.LV21/22.50, IT.LV17/18.AM, IT.LV17/18.CP, S9.TSK3.NS, S9.TSK3.PRA, S10.TSK3.NS, S10.TSK3.PRA, TV.LV21/22.51, TV.LV21/22.52, TV.LVALG.56 25. ANS: v

a. 200

–80 –40 40 80 t

b. –2°C

DIF: L2 REF: 7-8 Graphing Radical Functions OBJ: 7-8.1 Radical Functions STO: MD 2.1.3 TOP: 7-8 Example 5 KEY: domain,graphing,range,radical function,multi-part question,problem solving,word problem MSC: NAEP A2a, CAT5.LV21/22.53, CAT5.LV21/22.56, IT.LV17/18.AM, S9.TSK3.DSP, S9.TSK3.GM, S10.TSK3.DSP, S10.TSK3.GM, TV.LV21/22.14, TV.LV21/22.15, TV.LVALG.56