Reference no: EM131550392

1. Consider the piecewise function f(x)= {(9x+2 for 1≤x≤3 @8x+7& for 3<x≤6 @6x+5 & for 6<x≤9)¦

Calculate f (8). Show some work/explanation.
A. 74
B. 71
C. 53
D. 74, 71, and 53

2. Given f(x)=√(x-1)and g(x)=x-4, which of the following is the domain of the quotient function ? Explain.
A. (-∞,4)∪(4,∞)
B. [1,4)∪ (4,∞)
C. (1,∞)
D. [+ 1,∞) ¦

3. Let f(x)=x^3+1. Which of the following is true? Explain your answer.
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.

4. The time it takes to clean up after a party varies inversely with the number of people working on the job. If 4 people could complete the clean-up in 35 minutes, then how long (to the nearest minute) would it take for 7 people? Show work.
A. 16 minutes
B. 20 minutes
C. 32 minutes
D. 61 minutes

5. Suppose a gardener has 40 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.)
A. A(x) = 20x - x2
B. A(x) = 40x - x2
C. A(x) = x2 - 40x
D. A(x) = √(1600-x^2 )

6. 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.)

7. A graph of y = f (x) follows. No formula for fis given.

Which graph (A, B, C, or D) represents the graph of =f(x-1)-2?

BRIEFLY EXPLAIN how you have decided which graph is the correct one.

y = f(x) (below) (Grid supplied for scratch work; You are NOT required to submit your own graph)

8. no explanation required)

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

(a) 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?

(f) The piecewise function has many pieces. Write the formula for just ONE PIECE of this piecewise function. (You choose the piece you prefer. No explanation required)

f(x) = _2_ for _domain (-4, 0)_____ (state the x-values associated with your piece).

9. 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.

(c) Findthe composite function (f o g)(x) and simplify the results. Show work.

(d) Find (f o g)(3). Show some work.