College Algebra Review for Test 3
Name________________________
Solve the equation.
2x x
= +5
1)
5
3
Answer: {75}
2)
9x
x 7
-x=
4
32 8
Answer: {-
28
}
39
3) -10 - 3(2x + 1) = 8x + 1
Answer: - 1
Evaluate the function at the given value of the independent variable and simplify.
4) g(x) = 2x + 5; g(x + 1)
Answer: 2x + 7
Solve the equation by factoring.
5) 9x2 - 71x = 8
Answer: {-
1
, 8}
9
Find the inverse of the one-to-one function.
5x - 3
6) f(x) =
8
8x + 3
Answer: f-1(x) =
5
Evaluate the piecewise function at the given value of the independent variable.
7)
4x - 1 if x < -4
f(x) =
2x + 3 if x -4
Determine f(-5).
Answer: -21
1
Solve the radical equation, and check all proposed solutions.
8) x - 3x - 2 = 4
Answer: {9}
Determine whether the given function is even, odd, or neither.
9) f(x) = 4x2 + x4
Answer: Even
10) f(x) = x3 - 2x
Answer: Odd
11) y = x2 + 1
Answer: Even
Solve the equation by the square root method.
12) (2x + 3)2 = 25
Answer: {-4, 1}
Determine whether the equation defines y as a function of x.
13) y = -6x + 4
Answer: y is a function of x
14) y2 = 5x
Answer: y is not a function of x
Solve the inequality and answer using interval notation.
x
8
15) 5 + 1 2
Answer: (- , -4] or [8,
16) |x - 4| - 2
)
4
Answer: [-2, 10]
Solve and check the equation.
17) (x + 6)3/2 = 343
Answer: 43
2
18) 3x5/2 - 12 = 0
Answer:
5
16
3/4 - 7 = 20
19) (x2 + 4x + 4)
Answer: {-11, 7}
Solve the problem.
20) Use the graph of f to determine each of the following. Use interval notation.
a) the domain of f
b) the range of f
c) the x-intercepts or zeros of the function
d) the y-intercept
e) intervals on which f is increasing
f) intervals on which f is decreasing
g)intervals on which f is constant
h) the x-value at which f has a relative minimum. What is the value of relative (local)
minimum?
i) the x-value at which f has a relative maximum Whar is the value of the relative (local)
maximum?
j) the values of x for which f(x) = 2
k) f( -3)
3
l) the values for which f(x)
0
Answer: Local maximum: 0; local minimum: -4
Rationalize the denominator.
3
21)
5- 3
Answer:
15 + 3 3
22
Use possible symmetry to determine whether the graph is the graph of an even function, an odd function,
or a function that is neither even nor odd.
22)
Answer: Neither
23)
Answer: Even
4
Solve the equation using the quadratic formula. x =
-b ± b2 - 4ac
2a
24) x2 + 7x + 5 = 0
Answer:
25)
-7 - 29 -7 + 29
,
2
2
8
1
16
+4=
+
x
2x
3
Answer: {
45
}
8
Solve the equation by completing the square.
26) x2 + 14x + 34 = 0
Answer: {-7 - 15 , -7 + 15}
Solve the absolute value equation or indicate that the equation has no solution.
27) |4x + 8| + 2 = 4
Answer: {-
28)
5 3
,- }
2 2
21
3
+3=
x-3
x-3
Answer: {-3}
Solve the inequality and answer using interval notation.
29) 8x - 3 > 7x - 6
Answer: (-3,
)
Add or subtract as indicated and write the result in standard form.
30) (6 + 7i) - (-7 + i)
Answer: 13 + 6i
Determine the slope and the y-intercept of the graph of the equation.
31) 2x - 4y - 8 = 0
Answer: m =
1
; (0, -2)
2
5
Divide and express the result in standard form.
9
32)
7+i
Answer:
63 9
i
50 50
Graph the piecewise-defined function.
2 - x,
x 2
33) f(x) =
1 - 3x,
x>2
Answer:
Solve the equation
34) 2x4 = 250x
Answer: {0, 5}
Use the given conditions to write an equation for the line in slope-intercept form.
35) Passing through (8, 3) and (5, 7)
Answer: y = -
4
41
x+
3
3
6
Use the given conditions to write an equation for the line in the indicated form.
36) Passing through (2, 3) and parallel to the line whose equation is y = 2x - 6;
point-slope form
Answer: y - 3 = 2(x - 2)
37) Passing through (4, 5) and perpendicular to the line whose equation is y =
slope intercept form
Answer: y = - 3x + 17
Use the given conditions to write an equation for the line in point-slope form.
38) Passing through (2, 5) and (3, 8)
Answer: y - 5 = 3(x - 2) or y - 8 = 3(x - 3)
Find the product and write the result in standard form.
39) (9 + 7i)(9 - 7i)
Answer: 130
40) 4x3 + 3x2 = 100x + 75
Answer: {-5, -
3
, 5}
4
7
1
x + 6;
3