Download Unit 5 Review Worksheet

Secondary Math III
Name: ______________________________________________
Unit 5 REVIEW
Period: _______________
Simplify each problem. Express answers in simplest form (leave in factored form; do NOT multiply out). List
ALL DOMAIN RESTRICTIONS on all odd numbered questions. Show work.
1.
15𝑚𝑛7
10𝑚4 𝑛4
2.
3𝑥𝑦
𝑥𝑦+𝑥
3.
𝑥 2 +5𝑥+6
𝑥 2 −4
4.
𝑥 2 +2𝑥−3 𝑥 3 +𝑥 2
∙ 𝑥+3
𝑥2
5.
𝑥 2 +2𝑥−8
𝑥−2
÷ 3𝑥+3
𝑥 2 +4𝑥+3
6.
12𝑥+6
6𝑥 2 +9𝑥+3
÷
2
21𝑥 −21
7𝑥 3 −7𝑥 2
7.
5𝑥 3𝑥 2 +12𝑥
∙ 7𝑥−7
𝑥+4
8.
2𝑥
5𝑎𝑏3
+ 3𝑎2 𝑏2
9.
𝑥
𝑥+1
+ 3𝑥+6
𝑥 2 −4
10.
𝑥
2
− 2
𝑥 2 +5𝑥+6
𝑥 +4𝑥+4
11.
𝑥
𝑥+3
6𝑥
𝑥 2 −9
12.
𝑥
𝑥−𝑦
3
÷ 𝑥 2 −2𝑥+1
−
4𝑦
+
𝑦
𝑥 2 −𝑦 2
−
2𝑥
𝑥+𝑦
Solve each equation. Show all work. Simplify all answers. Remember to check for extraneous solutions.
13.
2(x + 5) – 7 = 3(x – 2)
14.
100−4𝑥
3
15.
2x2 = 19x + 33
16.
2
𝑥
= 4+𝑥
17.
5
6
18.
5
𝑥
+2 = 3
𝑥
= 𝑥−2 + 1
1
=
5𝑥+6
4
+6
2
1
Graph by finding the vertical and horizontal asymptotes without the use of a calculator. Then use your calculator and the
table of values to graph the curve.
𝑥
𝑥
19. 𝑦 = 𝑥−3
20. 𝑦 = 𝑥 2 −4
y
y











x













x




21.
Find ALL the zeros of the following polynomial. f (x) = 2x3 – 5x2 – 11x – 4 (REVIEW)
a.
Divide (2x3 – 5x2 – 11x – 4) ÷ (x – 4) using either long or synthetic division.
b.
Using the quotient you got from above, completely factor 2x3 – 5x2 – 11x – 4.
c.
What are the zeros of 2x3 – 5x2 – 11x – 4?
d.
What is the end behavior of f (x) = 2x3 – 5x2 – 11x – 4?
e.
Draw a rough graph of f (x) = 2x3 – 5x2 – 11x – 4.
f.
Solve and write your answer in interval notation: 2x3 – 5x2 – 11x – 4 > 0
g.
Solve and write your answer in interval notation: 2x3 – 5x2 – 11x – 4 ≤ 0
22. Graph the piecewise function:
𝑓(𝑥) = {
(𝑥 + 1)2 + 1, 𝑖𝑓 𝑥 > −1
−𝑥 + 1, 𝑖𝑓 𝑥 ≤ −1
23. Graph the piecewise function, then find the function values.
2𝑥 − 1, 𝑥 ≤ 0
𝑓(𝑥) = {1
𝑥 + 3, 𝑥 > 0
2
a. f(-2) =
b. f(0) =
c. f(2) =