Review
1. Solve. Simplify your answer as much as possible.
−21 = − 37 w
78 − u = 168
−5u − 18 = −2(u − 6)
w−4 w+1
−
=1
5
3
2. Solve for L.
3y − 8 = −20
w
w
+4=
3
2
−2 =
−
3x − 23
4
3
2
9
=− u−
2
7
5
3(w − 2) − 5w = −2(w + 3)
23 + 18y = −21 + 14y
9=
9y + 5 y − 6
+
8
2
5(2 − v) + 7v = 2(v + 1)
4LW = V
Solve for B.
A = 4B + C
Solve for x.
y = (x − 8)m
3. A house was increased in value by 34% since it was purchased. The current value is $335,000. What was the
value when it was purchased?
4. A TV has a listed price of $503.98 before tax. If sales tax is 7.5%, find the total cost of the TV with sales
tax included.
5. The perimeter of a rectangle is 132 feet. If the length is represented by 5y and the width by 4y + 3, find the
length and width in feet.
6. Solve the inequality. Graph your solution and write it in interval notation.
−4u + 37 ≤ 13
8w − 40 > −3(4 − 5w)
− 12 ≤ 4x + 4 < 16
7. Solve the following absolute value equations or inequalities. For the inequalities, graph your solutions and
write your solutions in interval notation.
|6v − 3| = 9
|4u + 2| − 35 = −5
|4x + 4| ≤ 8
|5v − 9| = |5v + 4|
|u − 2| > 6
8. Find the x-intercept and y-intercept for the following, and then use them to graph the functions.
2x + 4y = −8
y = − 14 x + 2
9. Find the slope and y-intercept, then graph.
−3x − 5y = −15
− 3x + 4y = −20
10. Find an equation for the line described. You can leave your answer in point-slope form or slope-intercept
form.
Line passing through the points (−9, −6) and (−4, 5).
Line passing through (−8, 2) with a slope of − 45 .
Line passing through (9, 6) and parallel to the line y = 32 x.
Line passing through the origin and perpendicular to the line y = 32 .
11. Owners of a recreation area are filling a small pond with water at a rate of 35 liters per minute. There are
700 liters in the pond when they begin.
Let W represent the amount of water in the pond (in liters), and let T represent the number of minutes the
water has been added.
Write an equation relating W to T , and the graph your equation.
12. The entire graph of the function h is shown in the figure below. Write the domain and range of h using
interval notation.
13. The graph of a function f is shown below.
Find f (2) and find one value of x for which f (x) = −3.
14. Find the domain of the function, and write your solution in interval notation.
√
√
√
g(x) = x − 4
f (x) = −x + 9
h(x) = 2x − 3
15. Solve the following system of equations.
y = 3x − 4
4x + 3y = 27
6x + 9y = −3
7x − 2y = −9
6x + 5y = 9
4x − 5y = −9
16. A jet travels 1464 miles against the wind in 2 hours, and it travels 1704 miles with the wind in the same
amount of time. What is the rate of the jet in still air, and what is the rate of the wind?
17. Hong bought a desktop computer and a laptop. Before financing charges, the laptop cost $400 less than the
desktop. He paid for the computers using two different financing plans. For the desktop, the interest rate
was 7.5% per year, and for the laptop, it was 8% per year. The total finance charge for one year was $371.
How much did each computer cost before finance charges?
18. Simplify as much as possible. Leave your answers with only positive exponents.
!3
− 4a
6u4 v 2
3 z 4 )2 (2x2 y 3 z)
5
5
4
3
2
(−x
2y v · 4v · 6y
(−7ab )
b3
18uv 2
4m4
3m7 n2
!2
4v −4
!3
2x−3 u
(x2 z −1 )
z −2
36x−4 y 3 z −2
6y −5 z 6
(−3w4 x−2 )3
(−9)−2
19. Factor.
2w3 + 5w2 + 14w + 35
4y 2 − 28y + 48
ux − 7x − 3u + 21
3y 2 − 4y − 7
y 2 − 10y + 16
3y 2 − 4y − 20
y 2 − 14y + 49
27w3 − 48w
w2 − 36
32u2 − 2u2 v 4
20. Solve.
3y 2 − 18y = 0
u2 − 10u + 21 = 0
5w2 = −17w − 6
21. Find all values of x that are NOT in the domain of the following functions.
f (x) =
3x
2x − 10
g(x) =
x2 + 2x − 63
x2 − 49
22. Simplify.
4u2 − 100
u2 − 8u + 15
x−8
x2 − 64
7(2w + 5)(w + 6)
21(w + 4)(2w + 5)
23. Perform the operation and simplify.
2y 9ay
·
3a 10y 5
4x − 20 9x − 8
·
45x − 40 2x − 10
c2 − 9c
3c + 8
+ 2
2
c − c − 12 c − c − 12
5
9
− 2
6y 8y
2
3
−
x−5 x+4
2
5y
2
3−
5y
15s4
3t5 u3
5rs2
9t2 u
x2 − 3x + 2 4x − 8
÷
x2 + 5x + 6
x+2
x−1
4x + 8
·
2
x −x−6 x−2
7−
1−
3x2
4
2
+ 2
+ 2x − 1 3x − 4x + 1
3
x+6
u−1
9
+x
x+6
1
− v2
24. Evaluate
1
1
1
27 3
256 4
1
81− 4
(−8) 3
25. Simplify.
1
5
7
w ·w
3
4
u2
u
√
6
7
√
75 − 3 27
√ √
√
√
( x − 2)( x + 2)
√
27u14
√
√
√
4z 32z + 18z 3
√
√
(x + 2 2)2
5z ·
√
3
p
8t5 y 8
54x13
√
√
3
7z
√
4
y·
12u2 ·
p
3
y2
√
3
40t8 w3
9u5
26. Solve. Remember to check your solutions.
√
√
√
3y + 18 + 2 = 5
5x + 10 = 7x − 12
√
11y − 30 = y
u−5=
√
49 − 8u
27. Perform the operation and simplify. Write your solution in a + bi form.
(6 − 2i) + (4 + 3i)
(3 − 7i) − (5 + 4i)
(−3 + 6i)(−4 + 3i)
4 − 2i
2 − 5i
28. Solve. You may need to use the quadratic formula.
(v − 7)2 − 32 = 0
(w + 9)2 − 45 = 0
4x2 − 9x + 3 = 0
3x2 + 5x = 3
29. A model rocket is launched with an initial upward velocity of 235
seconds is given by h = 235 − 16t2 .
2x2 + 5x − 1
2x2 − 3x + 6 = 0
ft
sec .
The rocket’s height h (in feet) after t
Find all values of t for which the rocket’s height is 151 ft.
30. Graph the following functions. Make sure to label the vertex.
g(x) = −2x2
h(x) = 3x2 − 1
y = (x − 1)2 − 3
31. State the vertex and x-intercepts of the following functions, then use them to graph the function.
y = x2 − 4x − 21
y = x2 − 8x + 12
32. Given f (x) = −2x2 + 16x − 34, answer the following.
Does the function have a minimum or a maximum value?
At what x value does the min/max occur?
What is the min/max value?
33. A supply company manufactures copy machines. The unit cost C (cost in dollars to make each copy machine)
depends on the number of machines made. If x machines are made, then the unit cost is given by C(x) =
0.5x2 − 170x + 25, 850. What is the minimum unit cost?
34. s(x) = 3x + 6
u(x) = x2 + 7
t(x) = 4x
w(x) =
√
x+8
Given the functions defined above, find the following expressions.
(s · t)(x)
(s + t)(x)
w(u(x))
w(u(1))
(s − t)(4)
u(w(1))
35. For each pair of functions below, find f (g(x)) and g(f (x)). Then determine whether f and g are inverses of
each other.
x+7
6
f (x) =
f (x) = 2x + 3
f (x) =
x
5
6
g(x) =
g(x) = 2x − 3
g(x) = 5x − 7
x
36. h is a one-to-one function. Find h−1 (x).
h(x)4x + 3
37. f is a one-to-one function, f (x) =
h(x) = 5x3 + 7
√
x + 5 + 4.
Find the domain and range of f (x). Then find f −1 (x) and its domain.
h(x) =
√
3
2x + 5