College Algebra

Instructions: This quiz covers through week 4. You may either type your answers and submit as a word doc or use pencil and paper and scan your work and submit. In either case, submit your work to the solutions folder in the classroom. It is best to show your work so that you can receive partial credit. If the answer is incorrect and there is no work to back up the answer then the answer will receive zero points. By showing you understand the process you will receive some credit even for an incorrect answer.

1. Given f(x) = √(x-2) and g(x)=x-4, which of the following is the domain of the quotient function f/g? Explain. 1._______

A. (-∞,4)∪(4,∞)
B. [2,4)∪ (4,∞)
C. (2,∞)
D. [2,∞)

2. Let f(x)=5x⁷+1. Which of the following is true? Explain your answer. 2. ______

A. f is an even function.
B. f is an odd function.
C. f is both even and odd.
D. f is neither even nor odd.

3. Suppose a gardener has 60 yards of fencing to make a rectangular garden enclosure. If the enclosure is x yards long, express the area A of the enclosure as a function of the length x. Briefly explain your choice (You may find it helpful to draw a picture, but it is not necessary to submit it.)

3. _______

A. A(x) = 30x - x²
B. A(x) = 60x - x²
C. A(x) = x² - 30x
D. A(x) = √(3600-x² )

4. For each graph, is the graph symmetric with respect to the x-axis? y-axis? origin?(No explanation required. Just answer Yes or No to each question.)

(a)

Symmetric with respect to the

x-axis? ____

y-axis? ____

origin? ____

(b)

Symmetric with respect to the

x-axis? ____

y-axis? ____

origin? ____

(c)

Symmetric with respect to the

x-axis? ____

y-axis? ____

origin? ____

5. Consider the graph of the piecewise function y = f (x) pictured below.

State the value of f (-2).

(b) State the domain of the piecewise function.

(c) State the range of the piecewise function.

(d) State the interval(s) on which the function is increasing. That is, for what x-values is the function increasing?

(e) State the interval(s) on which the function is decreasing. That is, for what x-values is the function decreasing?

6. Let f(x) = 2x² - 5x + 1 and g(x) = 1 - x.

(a) Find the difference (f -g)(x) and simplify the results. Show work.

(b) Find (f -g)(-1) and simplify the results. Show work.