Form A
Tennessee State University
Department of Mathematical Sciences
Math 1710 - Final Exam Review
If f ( x ) = - x2 - x - 6, find f ( -3 ).
1.
a.
f ( -3
3 ) = 10
b. f ( -3 ) = 8
c. f ( -3 ) = - 18
Determine whether f is even, odd, or neither even nor odd. f (x)) = x 3 + 4 x
2.
a. f is even
3.
b. f is odd
c.
Graph the function f (x) = | x | + 8
a.
b.
c.
4.
d. f ( -3 ) = - 12
Find the inverse function of f ( x ) = 2 x + 7
f is neither even nor odd
5.
a.
b.
c
d.
Let f (x) = 5 x + 2, g (xx) = x 2. Find:
a.
b.
c.
d.
6. Find the standard equation of any parabola that has vertex V(-1, 5).
a. y = a(x - 5) 2 + 1
c. y = (ax - 2) 2 + 5
b. y = (x + 1) 2 - 5
d. y = a(x + 1) 2 + 5
7. Simplify the difference quotient given:
a.
8.
9.
− 12
x−a
b.
x
x−a
f(x) =x 2 - 6, then
c. − f ( x)
f ( x + a ) − f (a)
=
x−a
d.
x 2 − 2ax
x−a
Express in terms of logarithms of x, y. log 7 ( xy )
a. log 7 ( x ) - log 7 ( y )
b. log 7 ( x ) + log 7 ( y )
c. log 6 ( x ) + log 6 ( y )
d. ln ( x ) + ln ( y )
Find the third term of the sequence { 17 - 6 n } .
a.
a3 = 17
b. a3 = 23
c. a3 = 23
d. a3 = -1
-
10. Which graph below represents: f (x) = 2x 3 −1
a.
b.
c.
11.
Find vertical and horizontal asymptotes of the function:
a.
b.
c.
d.
12.
13.
Find the standard equation of any parabola that has vertex V(-6,
V( 6, 7).
a.
y = (x + 6) 2 - 7
b. y = a(x + 6) 2 + 7
b.
y = (ax - 12) 2 + 7
d. y = a(x - 7) 2 + 6
Find the minimum value of the function f (x) = x2 + 6 x + 16
a. f (-3) = 7
14 .
b. f (7) = 3
c.
f (2) = 6
Find all values of x such that f (x) < 0. f (x) = 36 x - x3
a.
b.
d. f (0) = 16
c. None of these
15.
Use synthetic division to find f ( c ): f ( x ) = 5 x 3 + 9 x 2 - 6 x + 3 , c = 2
a. f ( 2 ) = 76
16
d.
b. f ( 2 ) = 64
x = 0 , multiplicity 1, x = 3 , multiplicity 2,
b.
x = 3 , multiplicity 2
c.
d.
x = 3 , multiplicity 2,
x = 0 , multiplicity 1, x = 3 , multiplicity 2,
An investment of $884 increased to $8387 in 15 years. If the interest was compounded
continuously, select the best equation below that can be used to find the interest rate.
a.
(
)15
b.
r = $8387e15
(
)15
d.
$8387 = $884e15r
$884 = $8387 1 + 15r
c.
$8387 = $884 1 + 15r
18.
Solve the equation.
a.
19.
d. f ( 2 ) = 67
Find the zeros of f (x),
), and state the multiplicity of each zero.
a.
17.
c. f ( 2 ) = 3
x=2
b.
Solve the equation.
a.
12
b.
x=3
c.
x=4
d.
x=-2
log 2 (x - 4) = 3
18
c.
10
d. 7
20. Find the domain of f
a.
c.
21.
b.
d.
Find the sum
a.
S = 35
b
S = 39
c.
S = 37
S = 22
Find the specified term of the arithmetic sequence that has the two given terms.
22.
a1 :
a.
a1 = 14
a8 = 44, a9 = 50
b.
a1 = 8
c.
a1 = 1
23.
Find the intervals on which f is decreasing.
b.
d.
a.
c.
.
24. Find the partial fraction decomposition.
a.
b.
c.
d.
25. Express in terms of logarithms of x, y, z, w.
a.
b.
c.
d.
d.
5log 4 ( x ) + log 4 ( w ) + 3log 4 ( y ) + 4log 4 ( z )
log 4 ( x ) + log 4 ( w ) - log 4 ( y ) + log 4 ( z )
5log 4 ( x ) + log 4 ( w ) - 4log 4 ( y ) - 3log 4 ( z )
5log 4 ( x ) + log 4 ( w ) - 3log 4 ( y ) - 4log 4 ( z )
d.
a1 = 2
26.
Solve the equation. log 6 ( 3 x - 17 ) = log 6 ( 28 ) - log 6 ( 4 )
a.
27.
x=5
b.
x = 10
c.
x = 13
d.
x=8
Find a polynomial f (x)) of degree 3 that has the indicated zeros and satisfies th
the given
condition.
4, - 1, 3 ; f ( 0 ) = 36
a.
b.
c.
d.
28.
Find the partial fraction decomposition:
a.
b.
c.
29.
d.
Find the sixth term of the geometric sequence : 4, 16, 64, 256,...
a.
4096
b.
5460
c.
4132
d.
16420
30. Given that P varies jointly with r and s and P = 7 when r = 3 and s =6, find P when
r = 9 and s = 24.
a.
P = 84
b. P = 9
c. P = 3
d. P = 24
31.
The price of admission to a high school play was $3 for students and $4 for non students. If
300 tickets were sold for a total of $104
$1043, how many non-students
students tickets were purchased?
a. 128 non-students
students
b. 162 non-students
c. 143 non-students
students
d. 172 students
32. The distance that an object will fall in t seconds varies directly with the square of t. An object
falls 3 feet in 1 second. How long will it take to fall 27 feet?
a. t = 27 sec
b. t = - 3 sec
c. t = 3 sec
d. t = 9 sec
33. Let f (x) = 7 x + 7, g (x) = x 2. Find:
a.
d.
34.
b.
e.
Find the third term of the sequence
a. a3 = -10
35.
c.
{ 10 - 5 n } .
b. a3 = 15
c. a3 = -5
Find the sixth term of the geometric sequence :
a. 19530
b. 15625
c. 78073
d. a3 = 10
5, 25, 125, 625,...
d. 15573
e. 78125
36.
a.
b.
c.
d.
37. Find the inverse function of
a.
b.
c.
d.
a.
b.
c.
28 Fins a polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zero and
degree.
38.
Solve the system of equation for x:
a.
x = 3, 5
y = x2 − 4

 y = 2x − 1
b. x = -1 , -3
c.
x = -2,
2, 1
d. x = -1, 3
39. If one zero of f (x) = x3 - 2 x2 - 25 x + 50 is k = 2, find two other zeros.
a.
b.
c.
40. Write the expression as one logarithm. log 7 ( 9 z ) - log 7 ( x )
a.
b.
c.
d.