# Project #7375 - Algebra

See attachment - please complete work in document.

1. (5 pts) Simplify:         Show some work.                                       1. ______

A.

B.

C.

D.

2. (5 pts)  Solve and write interval notation for the solution set. Show work.         2. ______

or

A.     (10, ¥)

B.     (10, 18]

C.     (–¥, 18] È (10, ¥)

D.     (–¥, 10) È [18, ¥)

3. (5 pts) Consider the piecewise function

Calculate f (6). Show some work/explanation.                                                                3. ______

A.        10

B.        30

C.        36

D.       10, 30, and 36

4. (5 pts) Which of the following is TRUE about the line through the points (–3, –1) and (–3, 1)? EXPLAIN/SHOW WORK.                                                                                          4. ______

A.     The slope is undefined.

B.    The slope is 0.

C.     The slope is negative.

D.     The slope is positive.

5. (5 pts) Given    and , which of the following is the domain of the quotient function?    Explain.                                                                         5._______

A.

B.

C.

D.

6. (5 pts)  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.                                                6.______

A.        16 minutes

B.        20 minutes

C.        32 minutes

D.        61 minutes

7. (5 pts) A graph of y = f (x) follows. No formula for f is given.                                                7. _______

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

BRIEFLY EXPLAIN YOUR CHOICE.(Grid supplied for scratch work; You are NOT required to submit your own graph)

A.                                                                                         B.

C.                                                                                         D.

8. (5 pts) Let .Which of the following is true? Explain your answer.  8. ____

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.

9. (5 pts) Suppose a gardener has 80 feet of fencing to make a rectangular garden enclosure. If the enclosure is x feet 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.)

9. _______

A.     A(x) = x2 – 20x

B.     A(x) = 40xx2

C.     A(x) = 80xx2

D.     A(x) =

10. (2 pts) 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? ____

11. (6 pts) Simplify . Show some work.

12. (6 pts) Find the slope-intercept equation of the line perpendicular to the line x + 4y = 20 and containing the point (12, –7).   Explain/show work.

13. (8 pts) Consider the points (–3, 7) and (19, 3).

(a) State the midpoint.

(b) If the point you found in (a) is the center of a circle, and the other two points are points on the circle, find the length of the radius of the circle. Find the exact answer and simplify as much as possible. Show work.

(c) State the equation of the circle described above (in standard form).

14. (9 pts)  Carl wants to purchase custom-made bumper stickers to advertise his business. Two websites offer different deals:

Website A:  Pay a fee of \$100.00, plus \$0.40 per bumper sticker

or        Website B:  Pay a fee of \$68.50, plus \$0.55 per bumper sticker

At least how many bumper stickers must Carl purchase in order for Website A to be the better choice? Note that “better” means cheaper! Show work.

Let x = number of bumper stickers. Write an appropriate inequality involving x and solve it algebraically. Write a sentence to carefully state the answer to the question. The sentence should have the form “Website A is the better choice if Carl purchases at least ____ bumper stickers.”

15. (12 pts, no explanation required) The graph of the function y = f (x) is pictured below.

 (a) State the domain of the piecewise function.     (b) State the range of the piecewise function.     (c) State the value of  f (3).

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

(e) 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) = ___________________  for __________________ (state the x-values associated with your piece).

16.  (12 pts)  Let  f (x) = 4x2 – 5x + 7 and  g(x) = 2 – 3x.

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

(b) Find the composite function  and simplify the results. Show work.

(c) Find . Show some work.

 Subject Mathematics Due By (Pacific Time) 06/09/2013 05:00 pm
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