Download Name___________________________________ Final Review

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Math 1314
Final Review
Write the number in standard form a + bi.
6 - -108
1)
2
Solve the equation.
16
2
=1+
14)
x+2
x-4
Find the sum or difference. Write the answer in standard
form.
2) (-2 - 3i) - (-9 + 9i) - (2 + 5i)
x+7+5=x
15)
16)
Find the product. Write the answer in standard form.
3) (7 - 6i)(9 - 9i)
3
x+4=6
17) 25x 4 - 61x2 + 36 = 0
4) i(6 - 2i)(7 - 5i)
Solve and graph the inequality. Give answer in interval
notation.
18) -6x + 12 > -7x + 17
Simplify the power of i.
5) i45
Find the quotient. Write the answer in standard form.
4 + 3i
6)
5 + 3i
19) 15 < 4x + 3 31
Solve the equation by the zero-factor property.
7) x2 + 2x - 15 = 0
Solve the quadratic inequality. Write the solution set in
interval notation.
20) x2 + 4x + 3 > 0
8) 7x2 + 4x - 3 = 0
Solve the rational inequality. Write the solution set in
interval notation.
x-7
0
21)
x+8
Solve the equation by the square root property.
9) (5x + 6)2 = 9
Solve the equation by completing the square.
10) x2 - 8x - 33 = 0
Solve the equation.
22) |2x - 8| = 5
Solve the equation using the quadratic formula.
11) 3x2 + 12x + 2 = 0
Solve the inequality. Write the solution set in interval
notation.
23) |5 - 4x| > 8
Solve the problem.
12) Find two consecutive even integers whose
product is 24.
24) x + 2 < 4
For the points P and Q, find the distance d(P, Q).
25) P(7, 5), Q(-4, -7)
13) A ladder is resting against a wall. The top of
the ladder touches the wall at a height of 9 ft.
Find the length of the ladder if the length is 3 ft
more than its distance from the wall.
For the points P and Q, find the coordinates of the
midpoint of the segment PQ.
26) P(0, 1), Q(8, 8)
1
Find the center and radius of the circle.
27) x2 + y2 + 8x - 10y - 8 = 0
Evaluate.
41) Find (f - g)(5) when f(x) = -2x2 + 5 and g(x) =
x - 6.
Give the domain and range of the relation.
28) y = (x + 1)2 - 1
29) y =
42) Find
f
(-2) when f(x) = 4x - 7 and g(x) = 4x2
g
+ 14x + 2.
2+x
43) Find (fg)(2) when f(x) = x - 1 and g(x) = -5x2
+ 14x + 7.
Evaluate the function.
30) Find f(3) when f(x) = 2x2 - 2x - 5
Find the requested function value.
Write an equation for the line described. Give your
answer in slope-intercept form.
31) horizontal, through (3, -5)
44) Find (f g)(3) when f(x) = 7x - 6 and g(x) = 5x2
- 7x - 6.
Find the domain and range of the function.
45) f(x) = x2 + 10x + 15
32) vertical, through (2, -1)
33) through (3, 9) and (0, -4)
Find the equation of the axis of symmetry of the parabola.
46) y = x2 - 8x + 24
Write an equation for the line described. Write the
equation in the form specified.
34) perpendicular to -5x + y = 7, through (4, 3);
slope-intercept form
Identify the vertex of the parabola.
47) y = x2 - 6x + 10
35) parallel to -6x + 5y = -87, through (7, -7);
slope-intercept form
Solve the problem.
48) A coin is tossed upward from a balcony 380 ft
high with an initial velocity of 16 ft/sec. During
what interval of time will the coin be at a
height of at least 60 ft?
Find the requested value.
7x + 7, if x 0
36) f(4) for f(x) = 2 - 3x, if 0 < x < 3
x,
if x 3
Use synthetic division to perform the division.
x 3 - x2 + 4
49)
x+2
Suppose the point (2, 4) is on the graph of y = f(x). Find a
point on the graph of the given function.
37) y = f(x + 3)
Express f(x) in the form f(x) = (x - k)q(x) + r for the given
value of k.
50) f(x) = 3x3 - x2 + 2x + 5; k = -1
Determine if the function is even, odd, or neither.
38) f(x) = -6x3 + 5x
Factor f(x) into linear factors given that k is a zero of f(x).
51) f(x) = x3 - 3x2 - 25x + 75 ; k = 5
Determine whether the equation has a graph that is
symmetric with respect to the y-axis, the x-axis, the origin,
or none of these.
39) y = 2x2 - 3
Find all rational zeros and factor f(x).
52) f(x) = x3 + 6x2 - 9x - 54
Determine if the function is even, odd, or neither.
40) f(x) = x4 - 4x2 - 5
Find any vertical asymptotes.
(x - 9)(x + 4)
53) h(x) =
x2 - 9
2
Find the horizontal asymptote of the given function.
16x2
54) h(x) =
8x2 - 3
Solve the equation.
66) log5 (x + 2) + log5 (x - 2) = 3
Solve the system by elimination.
67) x + 8y = 44
-4x + 7y = 19
Give the equation of the oblique asymptote, if any.
x2 + 2x - 3
55) f(x) =
x-4
Solve the system. If the system has infinitely many
solutions, write the solution set with x arbitrary.
68) 8x - 10y = 1
-16x + 20y =1
Determine whether or not the function is one-to-one.
56) f(x) = x2 + 7
If f is one-to-one, find an equation for its inverse.
57) f(x) = 7x - 4
Use the Gauss-Jordan method to solve the system of
equations. If the system has infinitely many solutions,
give the solution with y arbitrary.
69) 2x + 6y = 8
5x + 7y = -4
Find the function value. If the result is irrational, round
your answer to the nearest thousandth.
58) Let f(x) = 6 x. Find f(3).
Use the Gauss-Jordan method to solve the system of
equations. If the system has infinitely many solutions, let
the last variable be the arbitrary variable.
70) 6x + 9y - z = 101
x - 9y - 2z = -64
9x + y + z = 74
Solve the equation.
59) 16x - 2 = 324x
Find the future value.
60) $3933 invested for 4 years at 5% compounded
quarterly
Evaluate the logarithm.
1
61) log
8 64
Solve the equation.
62) log5 x = -2
Write the expression as a sum, difference, or product of
logarithms. Assume that all variables represent positive
real numbers.
63) loga(8x5 y)
Use the product, quotient, and power rules of logarithms
to rewrite the expression as a single logarithm. Assume
that all variables represent positive real numbers.
8
4
64) logn 9y + logn (81y2 )
5
3
Use the change of base rule to find the logarithm to four
decimal places.
65) log4 2
3
Answer Key
Testname: MATH1314FINALREVIEWFALL2016
1) 3 - 3i 3
2) 5 - 17i
34) y = -
3) 9 - 117i
35) y =
4) 44 + 32i
5) i
29
3
i
+
6)
34 34
3
9
,5
5
43) 15
44) 120
45) Domain: (- , ); Range: [-10, )
46) x = 4
47) (3, 1)
48) 0 t 5
-8
49) x2 - 3x + 6 +
x+2
10) {11, -3}
-6 ± 30
11)
3
12) 4, 6 or -4, -6
13) 15 ft
14) {6, 10}
15) {9}
16) {212}
6
6
17) - , -1, 1,
5
5
50) f(x) = (x + 1)(3x2 - 4x + 6) - 1
51) (x - 5)(x - 3)(x + 5)
52) -3, -6, 3; f(x) = (x + 3)(x + 6)(x - 3)
53) x = 3, x = -3
18) (5, )
54) y = 2
55) y = x + 6
56) No
19) (3, 7]
20) (- , -3)
21) (-8, 7]
13 3
,
22)
2 2
23) - , -
6
77
x5
5
36) 4
37) (-1, 4)
38) Odd
39) y-axis only
40) Even
41) -44
3
42)
2
7) {-5, 3}
3
, -1
8)
7
9) -
1
19
x+
5
5
3
4
x+4
57) f-1 (x) =
7
(-1, )
58) 216
1
59) 2
60) $4797.83
61) -2
1
62)
25
13
,
4
24) (-6, 2)
25) 265
9
26) 4,
2
63) loga 8 + 5loga x + loga y
64) logn (9 64/15 y64/15)
65) 0.5000
66) { 129}
67) {(4, 5)}
68)
69) {(-5, 3)}
70) {(7, 7, 4)}
27) center: (-4, 5); radius: 7
28) domain: (- , ); range: [-1, )
29) domain: [-2, ); range: [0, )
30) 7
31) y = -5
32) x = 2
13
x-4
33) y =
3
4