Form B
Tennessee State University
Department of Mathematical Sciences
Math 1710 - Final Exam Review
1. If f ( x ) = -x2 - x - 9, find f ( -44 ).
a. f ( -4 ) = 1
b. f ( -4 ) = - 21
c. f ( -4 ) = - 29
d. f ( -4 ) = 4
2. Find the domain of f.
a.
b.
c.
d.
3.
Find the range of f:
a.
b.
4. Simplify the difference quotient
c.
, h ≠ 0 if
7
a.
b.
2
c.
2
d.
2
14
5. Determine whether f is even, odd, or neither even nor odd: f (x) = x 11 + 3 x
a.
b.
f is odd
f is even
c.
d f is both even and odd
f is neither even nor odd
f is neither even nor odd
6. Find the minimum value of the function: f (x) = x2 + 4 x + 16
a. f (-2) = 12
b. f (12) = 2
c. f (0) = 16
d. f (1) = 11
7. From a rectangular piece of cardboard having dimensions a =5 inches b = 11 inches, an open box is to
be made by cutting out an identical square of area from each corner and turning up the sides. Express
the volume V of the box as a function of x.
a.
b.
V = ( 5 - 2x )( 11 - 2x )
c.
V = 2x( 5 - x )( 11 - x )
d.
V = x( 5 - x )( 11 - x )
V = x( 5 - 2x )( 11 - 2x )
8. Sketch the graph of f:
a.
b.
c.
d.
9. Express the function: f (x)) = x2 - 8 x + 21 in the form a(x - h) 2 + k.
a.
2
b.
f (x) = -4(x - 1) + 5
c.
2
f (x) = (x - 7) - 3
2
f (x) = (x - 4) + 5
d.
2
f (x) = (x + 4) + 7
10. Let f (x) = 5 x + 2, g (x) = x 2. Find:
a.
b.
c.
d.
11.
a.
b.
c.
d.
12. Solve the equation below if f (x) = x 2 - 4, g (x) = x + 1.
13.
a.
b.
c.
d.
Find the inverse function of:
a.
b.
c.
d.
14. If one zero of f (x) = x3 - 5 x2 - 9 x + 45 k is 5, find two other zeros.
a.
c. x = -3,
3, x = 9
b.
d.
15. Find a polynomial f (x)) of degree 3 that has the indicated zeros and satisfies the given condition.
- 4, 3, - 2 ; f ( 0 ) = - 48
a.
b.
c.
d.
16. A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zero and degree. Express
f ( x ) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R.
4 + 5 i ; degree 2
b.
a.
c.
17.
d.
Sketch the graph of f..
a.
b.
d.
c.
18. Solve the equation:
a. 3
log 4 (x - 1) = 2
b. 9
c. 25
d. 17
19.
Solve the system
a.
( 0, 2 )
c.
no solution
20. Use the graph of y = ex to help sketch the graph of:
a.
b.
( 4, 0 )
d.
( 4, 0 ), ( 0, 2 )
x+3
f(x)=e
b.
c.
d.
21. 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.
(
r 15
15
)
b.
(
)15
d.
$884 = $8387 1 +
c.
$8387 = $884 1 + 15r
22.
Solve the equation:
a.
x=8
c.
x 1 = - 6, x 2 = - 8,
r = $8387e15
$8387 = $884e15r
b.
x 1 = 6, x 2 = 8
d.
x=6
23.
Express in terms of logarithms of x, y, z, w:
a.
b.
c.
d.
4log 3 ( x ) + log 3 ( w ) + 2log 3 ( y ) + 3log 3 ( z )
4log 3 ( x ) + log 3 ( w ) - 2log 3 ( y ) - 3log 3 ( z )
log 3 ( x ) + log 3 ( w ) - log 3 ( y ) + log 3 ( z )
4log 3 ( x ) + log 3 ( w ) - 3log 3 ( y ) - 2log 3 ( z )
24. Solve the equation:
a. x = 10
25. Solve the equation:
a. x = - 6
log 7 ( 4 x - 27 ) = log 7 ( 15 ) - log 7 ( 3 )
b. x = 8
c. x = 5
d. x = 13
log 2 ( x + 5 ) + log 2 ( x +6 ) = 1
b. x = - 4
c. x = 4
d. x = 6
26. Find the exact solution using common logarithms, and a two-decimal-place
two
place approximation of the solution
of the equation.
2
6-x
= 11
a.
b.
c.
d.
27. The price of admission to a high school play was $3 for students and $5 for non students. If 450 tickets
were sold for a total of $1898, how many student tickets were purchased?
28.
a. 259 students
b. 274 students
c. 181 students
d. 176 students
Find the partial fraction decomposition:
a.
c.
b.
29.
Find the sum :
b. S = 14
a. S = 18
c. S = 10
d. S = 4
30. Find the common difference for the arithmetic sequence with the specified terms.
a4 = 11, a11 = 25
c. d = 7
b. d = 2
a. d = 4
d. d = 9
31. Insert five arithmetic means between 10 and 34.
b.
a.
14, 18, 21, 24, 30
14, 18, 22, 26, 30
d.
c.
14, 16, 21, 26, 30
14, 16, 19, 26, 30
32.
Find the geometric mean of 2 and 162.
b. 18
a. 164
c. 82
d. 4
33. Find the constant of proportionality for the stated conditions: z is directly proportional to the sum of x
and y, and when z = 44, x = 6 and y = 5.
c. k = 4
b. k = - 4
a. k = 44
d. k = 6
34. Find the center and radius for the circle with the given equation:
a. Center C(− 1, 8), radius 5
b. Center C(− 1,−10 ), radius 7
c. Center C(− 1, −8), radius 7
d. Center C(1, −8), radius 5
35. Find the maximum or the minimum value of the function:
a.
36.
max, f (−2) = 13
b.
min, f (−2) = 13
c.
min, f (13) = 2
Solve the equation:
a.
x = −6
b.
x = 11
c.
x = −8
d.
x = 13
d.
max, f (0) = 17
37. Simplify the difference quotient
for
a.
b.
c.
d.
38. Sketch the graph of
.
a.
b.
c.
d.
39.
Find the zeros of
, and select the false statement below:
a. x = 2, multiplicity 2
c. x = -2, multiplicity 2
40.
b. x = 4, multiplicity 3
d. x = - 2, multiplicity 3
Find the partial fraction decomposition:
a.
10
8
+
x−4 x+5
b.
5
4
+
x−4 x+5
c.
5
8
+
x−4 x+5
d.
10
8
−
x−4 x+5