MATH QUIZ 6

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The quiz is worth 100 points. Each problem is worth 5 points.

1. Determine whether each of the following graphs represents a one-to-one

function.

(a)

(b)

(c)

(d)

2. For each part below, determine if an inverse for the given f( x )

exists. If an inverse exists, then please find the inverse.

Otherwise, write “NO INVERSE”.

(a) f( x ) = 3x + 3

(b)

(c) f( x ) = 7

(d) f( x ) = 5x2 + 4x

3. In order to check to make sure we have the right inverse for a

given f( x ), we can check that and also that

. Using that idea of checking, please check to 　　

　　 make sure that the inverse you got in #2 (a) is the correct inverse

for f( x ) = 3x + 3.

4. The following formula can be used to convert Fahrenheit temperatures

x to Celsius temperatures T(x):

a) Find T(-13) and T(86).

b) Find T-1(x) and explain what it represents.

5. Please choose which equation represents the following graph:

A. f( x ) = -ex

B. f( x ) = -ex + 1

C. f( x ) = e-x + 1

D. f( x ) = ex – 1

6. Please choose which equation represents the following graph:

A. f( x ) = 2x - 1

B. f( x ) = 2x - 1

C. f( x ) = -2x - 1

D. f( x ) = -2x - 1

7. Water initially at 130 degrees Fahrenheit is left in a room of temperature

70 degrees Fahrenheit to cool. After t minutes, the temperature T of the

water is given by

Find the temperature of the water 10 minutes after it is left to cool.

8. Suppose that $100,000 is invested at 4% interest, compounded

monthly. Find the amount of money in the account after 10 years.

9. Find each of the following, and round answer to the nearest 4 decimal places.

(a) e4

(b) e-2

(c) log 50

(d) log2 128

(e) ln 50

10. Find log4 50 using the change of base formula, and round answer to the

nearest 4 decimal places.

11. Students in an accounting class took a final exam and then took equivalent

forms of the exam at monthly intervals thereafter. The average score

S(t), as a percent, after t months was found to be given by the function

S(t) = 78 – 15 log(t + 1)

(a) What was the average score when the students initially took the

test?

(b) What was the average score after 4 months? after 24 months?

12. Express log 2x as a sum of logarithms.

13. Express as a product.

14. Express as a difference of logarithms.

FOR #15 AND #16, EXPRESS IN TERMS OF SUMS AND DIFFERENCES

OF LOGARITHMS.