Math 110 Test 3 Sections All Start date: 10/27/05 (1-10, 12-17, 20-35. 39) Late Fee: 10/31/05 2 PM Instructors: Lundberg, Robertson, Shwalb, Final Deadline: 11/2/05 Noon Webb, Wright, Rimmasch, Bell, Wadley, Hales, Broderick, Shelley, Henry 1. Find the domain of the composite function

!

f o g if

!

f (x) = ln(x " 8) and

!

g(x) = x3.

(a) x > 2 (b) x > –2 (c) x ≥ 2 (d) x < 2 (e) –2 < x < 2 (f) x > 8

2. Find the range of

!

f (x) =3x

x + 2.

(a) {y | y ≠ 2} (b) {y | y ≠ – 2} (c) {y | y ≠ 3} (d) {y | y ≠ – 3} (e) {y | y ≠ 3/2} (f) all real numbers 3. The equation

!

(e4)xex2

= e12 has two solutions. Find the sum of the two solutions.

(a) –5 (b) –4 (c) –3 (d) –2 (e) –1 (f) 0 4. Let

!

f (x) = 2x2

+ 5 and

!

g(x) = 3x + a . There are two values of a so the graph of

!

f o g crosses the y-axis at 23. Find the sum of the two values. (a) –3 (b) –2 (c) –1 (d) 0 (e) 1 (f) 2 5. Solve the equation

!

log3(x2"12x + 44) = 2 for x.

(a) x = –5 (b) x = 7 (c) x = 5 (d) x = 5 or x = 7 (e) x = 12 (f) x = –5 or x = –7 6. Select the function that best describes the given graph.

5

6

4

2

(a)

!

y = log2(x "1) (b)

!

y = 2x+1 (c)

!

y = 2x"1

(d)

!

y = 2"x+1 (e)

!

y = log2 x (f)

!

y = 2x

7. Solve the equation

!

3e4 x

= 2 for x.

(a)

!

x =ln3" ln2

4 (b)

!

x =ln2 " ln3

4 (c)

!

x = 4(ln2 " ln3)

(d)

!

x =ln3" ln2

ln4 (e)

!

x =ln2

4 ln3 (f)

!

x =ln3

4 ln2

8. Use the properties of logarithms to find the exact value of the expression

!

log2 25log516. (a) 4 (b) 5 (c) 6 (d) 7 (e) 8 (f) 9 9. Write the expression

!

2log4 5 + 3log4 3" log4 9 " log4 5 as a single logarithm. (a)

!

log4 3 (b)

!

log4 5 (c)

!

log4 9 (d)

!

log415 (e)

!

log4 27 (f)

!

log4 45

10. If

!

logax =1,

!

loga y = 4 , and

!

logaz = 2, then find

!

logax2y

z3

"

# $

%

& '

(a) –3 (b) –2 (c) –1 (d) 0 (e) 1 (f) 2 11. Solve for x given

!

log4 (x " 3) =1" log4 2. (a) x = –1 (b) x = 1 (c) x = 2 (d) x = 3 (e) x = 4 (f) x = 5 12. Solve the equation

!

e2x" 3e

x" 4 = 0 .

(a) x = ln 4 (b) x = 4 (c) x = 0 (d) x = ln 4 or x = 0 (e) x = 1 (f) x = 4 or x = 0 13. Solve the equation

!

ex

+ e"x

= 2 . (a) x = 0 (b) x = 1 (c) x = 2 (d) x = ln 2 (e) x = ln 2 or x = 0 (f) x = 1 or x = 0 14. If $500 is invested at a rate of 8% interest compounded quarterly, then the amount in dollars after 5 years is: (a)

!

500(1.08)5 (b)

!

500(1.08)20 (c)

!

500(1.02)5

(d)

!

500(1.02)20 (e)

!

500(1.32)5 (f)

!

500(1.32)20

15. How long would it take an amount of money to quadruple if it is invested at a rate of 5% compounded continuously? (a) ln 4 (b) 2 ln 4 (c) 5 ln 4 (d) 10 ln 4 (e) 20 ln 4 (f) 25 ln 4

16. A certain amount of radioactive material decays according to the function

!

A(t) = A0e".2t where time is measured in hours. What is the half-life of the material in

hours? (a) ln 2 (b) 2 ln 2 (c) 5 ln 2 (d) 10 ln 2 (e) 20 ln 2 (f) 25 ln 2 17. Write an equation for the parabola.

4

2

-2

- 5 -2 2

(a)

!

y = x2

+ 2x +1 (b)

!

y = x2

+ x "1 (c)

!

y = 2x2" 4x +1

(d)

!

y = x2

+ 4x (e)

!

y = x2

+ 2x (f)

!

y = 2x2

+ 4x +1 18. Find the vertex of the parabola

!

y = x2

+ 6x +14 . (a) (–3, 5) (b) (3, –5) (c) (0, 14) (d) (–3, 14) (e) (5, –3) (f) (3, 41) 19. Find the equation for a parabola with directrix y = 2 and focus (–3, 4). Solve for y.

(a)

!

y =x2" 6x + 21

4 (b)

!

y =x2" 6x + 9

4 (c)

!

y =x2

+ 6x + 21

4

(d)

!

y =x2" 6x + 21

2 (e)

!

y =x2

+ 6x + 21

2 (f)

!

y =x2

+ 6x + 9

2

20. Solve the equation ln(x – 6) – ln(x –1) = ln(x – 4) – ln(x + 2). (a) x = 12 (b) x = 13 (c) x = 14 (d) x = 15 (e) x = 16 (f) x = 17

Answers

1. A 2. C 3. B 4. D 5. D 6. C 7. B 8. E 9. D 10. B 11. F 12. A 13. A 14. D 15. E 16. C 17. F 18. A 19. C 20. E