RED { DO NOT WRITE ON THIS EXAM
RED ? DO NOT WRITE ON THIS EXAM
Math 110 Test 3 Winter 2017
Sections 6?19, including the Salt Lake Center March 9?15, 2017
Instructors: Daniele D'Apuzzo, Joseph Chenworth, Tim Dolbin, Tara Lewis, Marica Riddle, and Jackie Robertson.
Instructions: Calculators and notes are not permitted. Please ensure that your responses are properly recorded on the bubble sheet. You may NOT write on this exam. There is no
time limit.
x
4
1. Given f (x) =
and g(x) = - , what is the domain of f [g(x)]?
x-1
x
(a) {x | x = 1, x = 0}
(b) {x | x = 4}
(c) {x | x = 0}
(d) {x | x = -4, x = 0}
(e) {x | x = 1, x = 0}
2. Given f (x) = 3x + 1 and g(x) = x2, find g[f (x)].
(a) 3x2 + 1 (e) 9x2 + 6x + 1
(b) 9x2 + 3x + 1
(c) x2 + 3x + 1
(d) 3x2 + 6x + 1
3.
Find
f -1(x)
of
f (x)
=
2x
+
3 .
x+2
2x + 3 (a)
x-2
x+2 (b)
2x - 3
2x + 3 (e)
x+2
-2x + 3 (c)
x-2
x-2 (d)
2x - 3
4. Find f -1(x) of f (x) = log5 x.
(a) x = y5 (e) y = x7
1 (b) y =
5x
(c) y = 5x
(d) xy = 5
5. Solve the equation for x. 8-x+14 = 16x.
(a) 2
(b) 6
(c) -4
(d) -2
(e) 4
6. Solve the equation for x. (e4)x ? ex2 = e12.
(a) {3, 4} (e) {-6, -2}
(b) {-2, 6}
(c) {-3, 4}
(d) {-6, 2}
x
7.
Find the domain of the function 3 - 2 log4
-5 . 2
(a) (10, )
(b) (0, )
(c) [10, )
(e) [0, )
(d) (5, )
8. Change the logarithmic statement to an equivalent statement involving an exponent 1
log2 8 = -3.
(a) 23 = -8 (e) (-2)-3 = -8
(b) 2-3 = 1 8
(c) (-3)2 = 1 8
1 -3 (d) 2 =
8
9. Write the expression as a sum and/or difference of logarithms. ln(xex)
(a) ln x - ex (e) 1 - ln x
(b) x ln x - e
(c) ln e - xx
(d) ln x + x
10. Find the equation of the parabola given: Vertex (2, -3) focus (2, -5).
(a) (x - 2)2 = -8(y + 3) (d) (x - 5)2 = 3(y + 2)
(b) (y + 3)2 = 6(x - 2) (e) (y - 2)2 = -8(x + 3)
(c) (x + 3)2 = 8(y - 2)
11. Consider the following graph:
y 16 12 8 4
-6 -4 -2 -4
2 4 6x
What is the equation of f (x)? (a) f (x) = 3x-4 (d) f (x) = log3(x - 4)
(b) f (x) = log3 x - 4 (e) f (x) = 3x+4
(c) f (x) = 3x - 4
x2 + 2x - 3
x2 + 7x + 6
12. Write the expression as a singular logarithm: log
- log
x2 - 4
x+2
(x - 3)(x + 1) (a) log
(x - 2)(x + 6)(x + 1)
(x - 2)(x - 6)(x + 1) (b) log
(x + 3)(x - 1)
(x - 2)(x + 3)(x - 1) (c) log
(x + 6)(x + 1)
(x + 3)(x + 1) (d) log
(x + 2)(x - 1)(x + 6)
(x + 3)(x - 1) (e) log
(x - 2)(x + 1)(x + 6)
13. Express y as a function of x. The constant c is a positive number. ln(y-3) = -4x+ln c.
(a) y = ce-3 + 4x (e) y = ce-4 + 3x
(b) y = ce-4x + 3
(c) y = ce-3x + 4
(d) y = ce-x + 7
14. Use properties of logarithms to find the exact value of the expression log2 6 ? log6 8.
(a) 2
(b) 4
(c) 6
(d) 3
(e) 8
15. Solve for x: 31-2x = 4x.
2 log 3 + log 4 (a)
log 3
(b) 2 + log 4
log 3 (e)
2 log 3 + log 4
2 log 3 - log 4 (c)
log 3
2 log 3 (d)
log 3 + log 4
16. How long in years would it take for an investment to double if compounded continuously at a rate of 2%?
(a) 2e50
(b) 50 ln 2
(c) .02 ln 2
(d) 2e.02
(e) 50e.02
ex - e-x
17. Solve the exponential equation for x:
= 2.
2
(a) ln(2 ? 5)
(b) ln(2 - 5)
(c)
(e) ln(4 ? 20)
ln(4 + 20)
(d) ln(2 + 5)
18. What rate of interest compounded annually is required to triple an investment in six
years?
(a) r = 6 3 + 1
(e) r = 3 - 1
(b) r = 3 6 - 1
(c) r = 3 + 1
(d) r = 6 3 - 1
19. Radioactive Decay Strontium-90 is a radioactive material that decays according to the function A(t) = A0e-0.0244t where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 500 grams
of strontium-90. What is the half-life of strontium-90?
ln 1/2 (a)
-0.0244
ln 1/2 (b)
0.0244
ln 45 (c)
-0.4244
ln 45 (d)
0.4244
ln 1/2 (e)
-0.0024
20. Find the equation that matches the graph
y 2
(1,1)
-2
2x
-2
(a) y2 = -4x (d) (y - 1)2 = -4(x - 1)
(b) (y + 1)2 = 4(y - 1) (e) (y + 1)2 = -4(y + 1)
(c) (y - 1)2 = 4(x - 1)
Answers: 1. D 2. E 3. C 4. C 5. B 6. D 7. A 8. B 9. D 10. A 11. C 12. E 13. B 14. D 15. E 16. B 17. D 18. D 19. A 20. C
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