Algebra 2/Trig
Name: ________________________________
CHAPTER 2 REVIEW
Evaluate each expression by using the order of operations.
1. 5 + 2(7 – 4)2
6 3
4. ( )
7
2. 36 x 52 – 3 x 42
3. 5 × 4 ÷ 2 + 3(4−1)
2 −2
3
5. 814
6. (− )
5
State the property that is used in each statement. All variables represent real numbers.
7. 5n x 1 = 5n
8. 7d – 14 = 7(d – 2)
9. (a + b) + c = (b + a) + c
10. 4(yz) = (yz)4
Simplify each expression. No negative exponents in your final answer! (Assume no variable equals 0).
11. y3(x2y)
3𝑝4 𝑞−1
14. (8𝑝−2 𝑞3 )-2
12. (9rt)2 (3rst)-3
15.
13.
14𝑟 2 𝑠−3 𝑡 4
35𝑟 −2 𝑠5 𝑡 3
(𝑥 5 𝑦 7 )(𝑥 4 𝑦 −3 )
(𝑥 5 𝑦 3 )2
1
16. The cost of enrollment at a community college is $120 plus $75 per credit, c, taken. Express the
college costs as a function of c and find the cost when 12 credits are taken. If Molly has a budget of
$1300 per semester for tuition. How many credits can she take?
State whether the following are functions, and if so give the domain and range.
17. {(5, 7), (7, 12), (9, 7), (11, 12), (13, 7)}
18. {(-2, 4), (0, 6), (-2, 8), (0, 10), (-2, 12)}
Evaluate each function for x = -2, and x = 0
19. f(x) = 5x2 – 4x + 7
20. f(x) =
𝑥2
2
+𝑥−4
For questions 21 – 26, let f(x) = 2x + 7 and g(x) = x - 9. Find new functions and state any domain
restrictions, if appropriate.
𝑔
21. f + g
22.
23. f ∙ g
24. g – f
Evaluate each composite function.
25. (𝑔 𝑜 𝑓)(3)
26. (𝑓 𝑜 𝑔)(2)
𝑓
2
27. Find the inverse for the function. State whether the inverse is a function.
{(1, 2), (5, 6), (2, 2), (6, 6), (3, 4)}
Find an equation for the inverse and state whether the inverse is a function.
28. f(x) =
3𝑥−8
29. f(x) = x4 – 3
4
30. f(x) = x – ½
31. Graph the function.
f(x) = {
2𝑥 + 5
𝑖𝑓 𝑥 ≤ 0
1
− 3 𝑥 + 3 𝑖𝑓 𝑥 > 0
Evaluate:
32. [4.5] + 3.5
33. [−1.7] + [1.7]
Identify each transformation from the parent function f to g.
34. f(x) = √𝑥,
𝑔(𝑥) = √𝑥 − 3
35. f(x) = x2, g(x) = (x + 3)2 – 4
3
Determine the equation of the transformed function.
36. The graph of f(x) = x2 is compressed horizontally by a factor of 1/2, reflected in the x-axis, and
translated 4 units downward.
37. Write the equations for the function shown below. (Assume all tick marks represent 1 unit).
a.
b.
c.
d.
4