Unit 4 Review
Integrated Math 3
Show all of your work on a separate piece of paper.
Sketch the graph of each function. Include the critical point, any asymptotes and/or the y-intercept.
1
1
2
−1
1) 𝑦 = 𝑥−3
2) 𝑦 = − 𝑥 + 1
3) 𝑦 = 𝑥+5 − 6
4) 𝑦 = 𝑥−2 + 4
5) 𝑦 = (𝑥 − 3)2 + 2
6) 3𝑥 − 6𝑦 = 12
7) 𝑦 = −(𝑥 + 2)3 − 4
8) 𝑦 = −|𝑥 + 2|
9) 𝑦 = −(𝑥 + 1)2 − 4
10) 𝑥 = −4
11) 𝑦 = −|𝑥 − 4| − 3
12) 𝑦 = − 𝑥−1 + 3
2
Simplify.
13)
16)
19)
22)
25)
28)
𝑥 2 +3𝑥+2
14)
𝑥 2 −3𝑥−4
𝑥 2 −2𝑥−8
2𝑥 2 −8𝑥
÷ 2𝑥 2 −10𝑥
𝑥 2 −2𝑥−15
𝑥 2 +4𝑥+3
÷
2𝑥 2 −11𝑥+5
𝑚4 −𝑛4
𝑚+𝑛
1
𝑏
𝑏
2𝑥−5
2
−
2𝑥−1
15)
2𝑥 2 −5𝑥+3
24𝑥𝑦 2
28𝑥 2
7𝑥
∙ 16𝑦
18)
20)
21)
23)
24)
2
+𝑎
𝑥+12
𝑥 2 +3𝑥
17)
𝑥 3 −𝑥 2
26) 𝑥 + 𝑥
3𝑥−2
2𝑥−5
5
29)
2𝑥
5
+
𝑥+1
27)
2𝑥 2 −1
10
−
𝑥
4𝑥+1
6
31)
− 𝑥+3
𝑥−2
32)
− 𝑥 2 +7𝑥+12
𝑥 2 −16
34)
1 1
−
𝑥 𝑦
2 3
+
𝑥 𝑦
35)
2
+𝑏
3𝑎
1
𝑎−
𝑏
30)
33)
36)
4𝑥+16 𝑥 2 +2𝑥−3
2𝑥+6
8
9
∙
𝑥+4
2 27
÷ 3 ∙ 16
𝑥 2 −𝑦 2
𝑥+𝑦
𝑥 2 −𝑦 2
𝑦−𝑥
1
𝑥2
2
+𝑥−𝑥
𝑥+2
𝑥 2 −2𝑥−15
1
−1
3
2 4
+
5 3
1
1
+
𝑚 2𝑚
3
𝑚−2
+
𝑥
𝑥+3
Solve for x.
37)
40)
43)
10
3
4
= 𝑥+2
1
2
38)
5
2
𝑎
+ 𝑐𝑥 = 𝑏
𝑥
1
39)
12
𝑥−4
+ 𝑥 2 −16 = 𝑥+4
41)
2
𝑥
44) 3𝑥 2 − 2𝑥 + 𝑐 = 0
+𝑎 =
𝑏
3𝑥
𝑐
𝑥−2
− 𝑥+4 = 𝑥 2 +2𝑥−8
42)
3
4
1
2
−3 = 𝑥+2
2𝑥−5
3𝑥+2
4
=5
45) 𝑝𝑥 2 + 𝑟𝑥 = 𝑛
46) Suppose one painter can paint the entire house in twelve hours, and a second painter takes eight hours to
paint the entire house. How long would it take the two painters together to paint the house?
47) Suppose you work in a lab. You need 20 liters of a 15% acid solution for a certain test, but your supplier
only ships a 10% solution and a 30% solution. Rather than pay the hefty surcharge to have the supplier make a
15% solution, you decide to mix 10% solution with 30% solution, to make your own 15% solution. How many
liters of 10% solution and 30% solution should you use?
48) Joe can paint the barn in 4 hours by himself. Steve has never timed himself painting a barn before so we
don’t know how fast he is. Working together, the two finish the job in 2.4 hours. How long would it take Steve
to paint the barn by himself?
Write the equation of the line described in any form.
49) (6,3) & 𝑚 = 3
50) contains points (−9,1) & (7, −2)
3
51) perpendicular to 𝑦 = − 5 𝑥 − 2 & through (−2,4)
52) parallel to 𝑥 − 4𝑦 = 8 & through (−2,4)
53) perpendicular to 5𝑥 + 3𝑦 = 6 & through (3, −1)
54) parallel to 𝑦 = − 3 𝑥 − 4 & through (5, −1)
55) tangent to the circle 𝑥 2 + 𝑦 2 = 25 through the point (−3, −4)
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