Unit 4: Practice Test
Algebra 2
Name ______________________________
Date _________________ Period _____
Read instructions carefully. Show all work.
Learning Target:
I will find the sum, difference, product, and quotient of functions.
I will find the composition of functions.
1. Find (𝑓 − 𝑔)(𝑥) for 𝑓(𝑥) = 2𝑥 + 7 and 𝑔(𝑥) = 𝑥 2 + 5𝑥.
1. ______________________
2. Given 𝑓(𝑥) = 𝑥 − 10 and 𝑔(𝑥) = 2𝑥 2 + 4, find 𝑓[𝑔(−4)].
2. ______________________
3. If 𝑓(𝑥) = 3𝑥 + 6 and 𝑔(𝑥) = 𝑥 2 − 2, find (𝑓 ∘ 𝑔)(𝑥).
3. ______________________
Learning Target:
I will find the inverse of a function.
I will determine whether two functions are inverses.
4. Determine whether each pair of functions are inverse functions.
1
a. 𝑓(𝑥) = 2𝑥 + 3 and 𝑔(𝑥) = 2 𝑥 − 3
4a. _____________________
b. ℎ(𝑥) = 𝑥 − 4 and 𝑘(𝑥) = 𝑥 + 4
4b. _____________________
Learning Target:
I will graph and analyze square root functions.
I will graph square root inequalities.
5. a) Graph 𝑦 = √𝑥 − 4 − 2.
b) State the domain and range of the function.
Domain: _______________
Range: ________________
6. Graph the square root inequality 𝑦 < √𝑥 + 1.
Learning Target:
I will simplify radicals.
5
7. Use a calculator to approximate √280 to three decimal places.
7. ______________________
8. Simplify: √64𝑥 8 𝑦 10
8. ______________________
3
9. Simplify: √432𝑎10 𝑏 5
9. ______________________
Learning Target:
I will simplify radical expressions.
I will add, subtract, multiply, and divide radical expressions.
10. Simplify: 3√98 + √128 − √45
11. Simplify:
3
10. _____________________
11. _____________________
√5−2
Learning Target:
I will simplify expressions involving rational exponents and radicals.
5
12. Write the expression √−32𝑎3 using rational exponents.
12. _____________________
2
13. Evaluate: 3433
13. ____________________
5
14. Simplify: 𝑥 −6
14. _____________________
Learning Target:
I will solve equations containing radicals.
I will solve inequalities containing radicals.
3
15. Solve: √7𝑥 + 8 = 4
15. _____________________
16. Solve: √5𝑎 + 1 + 4 < 10
16. _____________________
Unit 4 Practice Test – Multiple Choice
Name ____________________________________
Choose the letter of the correct response and darken the corresponding letter on your bubble sheet.
1. Find (𝑓 − 𝑔)(𝑥) for 𝑓(𝑥) = 2𝑥 + 7 and 𝑔(𝑥) = 𝑥 2 + 5𝑥.
A.
B.
C.
D.
– 𝑥 2 + 7𝑥 + 7
−𝑥 2 − 3𝑥 + 7
𝑥 2 + 3𝑥 + 7
𝑥 2 − 3𝑥 + 7
2. Given 𝑓(𝑥) = 𝑥 − 10 and 𝑔(𝑥) = 2𝑥 2 + 4, find 𝑓[𝑔(−4)].
A. 26
B. -38
C. 36
D. -28
3. If 𝑓(𝑥) = 3𝑥 + 6 and 𝑔(𝑥) = 𝑥 2 − 2, find (𝑓 ∘ 𝑔)(𝑥).
A. 3𝑥 2 − 6
B. 9𝑥 2 + 36
C. 3𝑥 2
D. 9𝑥 2 + 34
4. Determine whether each pair of functions are inverse functions.
1
Part a: 𝑓(𝑥) = 2𝑥 + 3 and 𝑔(𝑥) = 2 𝑥 − 3
Part b: ℎ(𝑥) = 𝑥 − 4 and 𝑘(𝑥) = 𝑥 + 4
A.
B.
C.
D.
Part a: YES; Part b: YES
Part a: YES; Part b: NO
Part a: NO; Part b: YES
Part a: NO; Part b: NO
5. a) Graph 𝑦 = √𝑥 − 4 − 2. b) State the domain and range of the function.
A.
B.
Domain: 𝑥 ≥ −4
Range: 𝑦 ≥ −2
C.
Domain: 𝑥 ≥ 4
Range: 𝑦 ≥ −2
D.
Domain: 𝑥 ≥ −4
Range: 𝑦 ≥ −2
Domain: 𝑥 ≥ 4
Range: 𝑦 ≥ −2
6. Graph the square root inequality 𝑦 < √𝑥 + 1.
A.
B.
C.
D.
5
7. Use a calculator to approximate √280 to three decimal places.
A. 16.733
B. 83.666
C. 3.086
D. 6.542
B. 32𝑥 4 |𝑦 5 |
C. 4𝑥 2 𝑦 3 √𝑦
D. 2𝑥𝑦√𝑥 2 𝑦 4
8. Simplify: √64𝑥 8 𝑦 10
A. 8𝑥 4 |𝑦 5 |
3
9. Simplify: √432𝑎10 𝑏 5
3
A. 6𝑎3 𝑏 √2𝑎𝑏 2
3
B. 7𝑎3 𝑏 √5𝑎𝑏 2
3
3
C. 6𝑎9 𝑏 3 √2𝑎𝑏 2
D. 7𝑎9 𝑏 3 √5𝑎𝑏 2
C. 18√2 − 3√5
D. 29√2 − 3√5
10. Simplify: 3√98 + √128 − √45
A. 34
B. 15√2 − 3√5
11. Simplify:
A.
3
√5−2
3√5−6
B. 3√5 + 6
9
C.
√5+2
3
D.
3√5+6
9
5
12. Write the expression √−32𝑎3 using rational exponents.
5
3
A. −32𝑎3
1
3
3
B. (−32𝑎)5
C. −325 𝑎5
D. −32𝑎 5
B. 228.7
C. 514.5
D. 49
2
13. Evaluate: 3433
A. 6352.4
5
14. Simplify: 𝑥 −6
A.
1
5
𝑥6
𝑥6
B.
𝑥
1
𝑥
5
C. 𝑥 6
D. −𝑥 6
C. 𝑥 = 4
D. no solution
C. 𝑎 < 7
D. 𝑎 > 7
3
15. Solve: √7𝑥 + 8 = 4
8
A. 𝑥 = 7
B. 𝑥 = 8
16. √5𝑎 + 1 + 4 < 10
1
A. 𝑎 ≥ − 5
1
B. − 5 ≤ 𝑎 < 7