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

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download