Find the domain of the function.
41) f(x) = 2x - 8
Answer: (- , 13]
42) f(x) = 4x2 + 9x + 7
Answer: (- ,
)
Multiply or divide as indicated.
x2 + 12x + 27
x2 + 3x
÷
43)
x2 + 16x + 63 x2 + 17x + 70
Answer:
x + 10
x
44) -14 - 3(2x + 1) = 8x + 1
Answer: - 1
Solve this equation.
45) 2x + 15 - x = 6
Answer: {-3}
46) x + 7 + 5 = x
Answer: {9}
47) f(x) =
x - 64
x2 - 12x + 27
Answer: x
3, x
9
48) -4x - 5 - 7(x + 1) = -6x - 6
Answer: {-
6
}
5
Rationalize the denominator.
2
49)
5- 2
Answer:
10 + 2 2
23
1
Find an equation of the line satisfying the conditions. Write the equation in slope-intercept form.
50) Through (-5, -2); perpendicular to -5x - 2y = 27
Answer: y =
2
x
5
Solve the inequality and answer using interval notation.
x
8
51) 5 + 1 2
Answer: (- , -4] or [8,
52) |x - 5| + 8
)
11
Answer: [2, 8]
Solve the system of equations.
53) 3x + y = 0
-3x + y = -6
Answer: {(1, -3)}
Solve the system of equations.
54) 8x + 12y = 12
7x - 2y = -2
Answer: {(0, 1)}
Find the product and write the result in standard form.
55) (1 + 4i)(1 - 4i)
Answer: 17
Add or subtract as indicated.
4
6
+
56)
x+ 1 x2 - 1
Answer:
10x - 8
(x - 1)(x + 1)(x - 2)
2
Divide and express the result in standard form.
9
57)
6+i
Answer:
54 9
i
37 37
Solve the equation by factoring.
58) 8x2 - 39x = 5
Answer: {-
1
, 5}
8
Find the midpoint of the line segment whose end points are given.
59) (2, 9) and (4, 8)
Answer: (3,
17
)
2
Solve and check the equation.
60) (x + 1)3/2 = 8
Answer: 3
Determine whether the equation defines y as a function of x.
61) y2 = 6x
Answer: y is not a function of x
Add or subtract as indicated and write the result in standard form.
62) (8 + 6i) - (-7 + i)
Answer: 15 + 5i
If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
63) f(x) = x3 - 5
3
Answer: f -1(x) = x + 5
For the given functions f and g , find the indicated composition.
64) f(x) = 4x2 + 6x + 3,
(g f)(x)
g(x) = 6x - 6
Answer: 24x2 + 36x + 12
3
Find the distance between the pair of points.
65) (2, -5) and (-3, -17)
Answer: 13
Solve the equation using the quadratic formula. x =
-b ± b2 - 4ac
2a
66) x2 + 7x + 7 = 0
Answer:
-7 - 21 -7 + 21
,
2
2
Use the given conditions to write an equation for the line in slope-intercept form.
67) Passing through (5, 7) and (7, 4)
Answer: y = -
3
29
x+
2
2
Solve the equation.
5x
x 7
-x=
68)
3
12 4
Answer: {- 3}
Solve the inequality and answer using interval notation.
69) 4x + 7 > 3x + 6
Answer: (-1,
)
4
Graph the linear function. Give the domain and range.
70) f(x) = -3x - 2
Answer: Domain: (- , )
Range: (- , )
Simplify using properties of exponents.
1/2
71) (25x4y8)
Answer: 5x2y4
Find and simplify the difference quotient
f(x + h) - f(x)
, h 0 for the given function.
h
72) f(x) = 9x2 + 6
Answer: 9(2x+h)
Solve the equation by the square root method.
73) (3x + 3)2 = 36
Answer: {-3, 1}
5
Solve the absolute value equation or indicate that the equation has no solution.
74) |7x + 8| + 9 = 13
Answer: {-
12 4
,- }
7
7
State the domain of the rational function.
(x - 2)(x + 9)
75) f(x) =
x2 - 9
Answer: (- , - 3)
76) f(x) =
(- 3, 3)
(3,
)
x-9
x2 + 7
Answer: (- ,
)
For the given function, find all asymptotes of the type indicated (if there are any)
(x - 3)(x + 5)
, vertical
77) f(x) =
x2 - 1
Answer: x = 1, x = -1
78) f(x) =
x+9
x2 + 4x + 2
, horizontal
Answer: y = 0
79) f(x) =
8x2 + 3
, horizontal
8x2 - 3
Answer: y = 1
6
List the x- and y-intercepts, and graph the function.
3x - 5
80) f(x) =
x-2
Answer: x-intercept:
5
5
, 0 , y-intercept: 0,
3
2
7