Name:
Period:
A
College Algebra: Spring Final Exam (No Calculators)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the amount that results from the investment.
1) The half-life of silicon-32 is 710 years. If a sample presently contains 50 grams, which expression determines
how much silicon-32 material will remain after 1650 years?
ln(0.5)
A. 1650 ek where k = 710
B. 50 e710k where k = ln(0.5)
1650
C. 710 e1650k where k = D. 50 e1650k where k = ln(0.5)
50
ln(0.5)
710
E. None of the above.
2) Which of the following functions might have the graph shown in the illustration below?
A. f(x) = 10
x - 2
B. f(x) = 2
2
x + 4x + 4
C. f(x) = D. f(x) = 2
x2 + 4x - 5
1
2x2
E. None of the above.
Determine the horizontal or oblique asymptote of the given function.
3x4 - x2
3) g(x) = x3 - x2 + 1
A. y = 3x - 3
B. y = 3x + 3
C. y = 3
D. y = 3x
E. None of the above.
Solve the problem.
4) Which of the following polynomial functions might have the graph shown below?
A. f(x) = x2 (x - 2)(x - 1)
B. f(x) = x2 (x - 2)2 (x - 1)2
C. f(x) = x(x - 2)(x - 1)2
D. f(x) = x(x - 2)2 (x - 1)
E. None of the above.
Find the coordinates of the x - and y-intercepts of f.
5) f(x) = 7x 3 + 11x2 - 6x
A. (7, 0), (-2, 0), (0, 0)
3
B. ( , 0), (-2, 0), (0, 0)
7
3
C. (- , 0), (2, 0), (0, 0)
7
D. (
7
, 0), (-2, 0), (1, 0)
37
E. None of the above.
Find the inverse function of f. State the domain and range of f.
3x - 2
6) f(x) = x + 5
A. f -1 (x) = x + 5
2
; domain of f: {x x ≠ -5}; range of f: {y y ≠ }
3x - 2
3
B. f -1 (x) = 5x + 2
; domain of f: {x x ≠ -5}; range of f: {y y ≠ - 3}
3 + x
3x + 2
; domain of f: {x x ≠ -5}; range of f: {y y ≠ 5}
C. f -1 (x) = x - 5
D. f -1 (x) = 5x + 2
; domain of f: {x x ≠ -5}; range of f: {y y ≠ 3}
3 - x
E. None of the above.
2
Use the properties of logarithms to find the exact value of the expression.
7) log5 5 + log 36 15 - log36 5 - log7 49
A. 2
B. - C.
3
2
D.
1
2
1
2
E. None of the above.
Solve the inequality.
x + 20
8)
≤ 3
x + 6
A. (-∞, -6) or (1, ∞)
B. (-6, 1]
C. (-∞, 1] or (6, ∞)
D. (-∞, -6) or (20, ∞)
E. None of the above.
Find the indicated composite for the pair of functions.
6
8
9) (f ∘ g)(x): f(x) = , g(x) = x + 1
3x
A.
18x
3x - 8
B.
9x
4
C.
6
3x + 8
D.
18x
3x + 8
E. None of the above.
Write as the sum and/or difference of logarithms. Express powers as factors.
(4x 2 + 8) x2 - 1
10) ln x3 - x2 + 2x - 2
1
1
A. ln4 - ln(x - 1) + ln(x + 1)
2
2
1
3
B. ln4 - ln(x - 1) + ln(x + 1)
2
2
1
1
C. ln4 - ln(x + 1) + ln(x - 1)
2
2
1
D. ln4 -ln(x + 2) - ln(x - 1)
2
E. None of the above.
3