Algebra Homework
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Math 107-Quiz 5
I have completed this assignment myself; working independently and not consulting anyone except the instructor.
Write your name here:
Multiple-choice: Select the correct answer and write it in the space provided.
Do not show work; write only one of the letters A, B, C, or D.
01. (4 pts) Given, find . Ans: ____
A.
B.
C.
D. None of the above
02. (4 pts) Let and Find. Ans: ____
A.
B.
C.
D.
03. (4 pts) Find the formula for the inverse of the function: . Ans: ___
A.
B.
C.
D.
04. (4 pts) Solve the equation: . Ans: ____
A.
B.
C.
D.
05. (4 pts) Find Ans:____
A. 4
B.
C.
D.
06. (4 pts) Convert to an exponential equation: logx = 15 Ans: ____
A. x = e15
B. x15 = 10
C. x = 1510
D. x = 1015
07. (4 pts) Convert to a logarithmic form: 49 = 7x. Ans: _____
A.
B.
C.
D.
08. (4 pts) Convert to a logarithmic form: r = es. Ans: ____
A. logs = r
B. logr = s
C. lnr = s
D. lns = r
09. (15 pts) Consider the functions and .
(a) State the Domain of f(x)
(b) State the Domain of g(x)
(c) (6 pts) Find the composition and simplify the result.
(d) State the Domain of
10. (12 points) Which of the following functions are one-to-one? (No work required)
(a) f(x) = x2-1 one-to-one Yes ____, No ____
(b) f(x) = x3 one-to-one Yes ____, No ____
(c) f(x) =|x-1| one-to-one Yes ____, No ____
(d) f(x) = one-to-one Yes ____, No ____
11. (16 pts) Let .
(a) Find the Domain and Range of f(x).
(b) (6 pts) Find f-1, the inverse function of f. (Show work)
(c) Give the Domain and Range of f-1.
12. (18 pts) Let . (No work required)
(a) Which describes how the graph of f can be obtained from the graph of y = ex ? Choice: ________
A. Shift the graph of y = ex to the left by 1 unit and up by 2 units.
B. Shift the graph of y = ex to the right by 1 unit and up by 2 units.
C. Reflect the graph of y = ex across the x-axis and shift up by 2 units.
D. Reflect the graph of y = ex across the y-axis and shift up by 2 units.
(b) What is the domain of f ?
(c) What is the range of f ?
(d) What is the horizontal asymptote?
(e) What is the y-intercept? State the approximation to 2 decimal places (i.e., the nearest hundredth).
(f) Draw the graph of f, using a graphing utility.
13. (7 points) Compound Interest Formula: , P = principal; r = rate as a decimal; t the number of years; n the number it compounds each year.
Suppose an amount of $10,000 is deposited at 2.6% compounded quarterly. It will grow to what amount in 6 years? (Show work and give answer to the nearest cent)