College algebra quiz

1) 6 points 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? ____

2) 10 points. Graph the equation and find the equation of a parallel line that passes by point (-20, 0).

3) 6 points. Which of the following equations does the graph represent? Show work or explanation.

A. B. C. D.

4) 12 points. Consider the points (2, 0) and (5, –6).

(a) Find the slope-intercept equation of the line passing through the two given points. Show work.

b) Graph the line you found in (a), either drawing it on the grid in the previous problem #3, or generating the graph electronically and attaching it, or creating a table of sample points on the graph of the equation (include at least five points), and use them to help create a graph of the equation. (You may use the grid shown below, hand-draw and scan, or you may use the free Desmos graphing calculator described under Course Resource to generate a graph.

x	y	(x, y)

(c) Compare your line for this problem, #4, with the line in the previous problem #3. Are the two lines parallel, perpendicular, or neither parallel nor perpendicular? (The terms parallel and perpendicular are discussed on pages 166 and 167.) No explanation required – just state the answer.

5) 10 points. Determine the equation for the line on the graph sketched below.

6) 10 points. Wendy is on a weight control program. Wendy´s weight w in pounds t weeks after the start of the program is modeled by w(t) = –0.022t2 – 0.20t + 235 for 0 t 20 weeks.

(a) What was Wendy´s weigh when she started?

(b) What is the average rate of change of Wendy over the interval [0, 20]. Show work and interpret results.

7) 20 points. Thomas is in the market to buy a special Christmas gift for all the members of his family. He asked quotations to two different people, and the following are the proposals:

Proposal 1: Pay a design fee of $40.00, plus $2.50 per gift

or Proposal 2: Pay a design fee of $62.00, plus $2.20 per gift

(a) State a linear function f (x) that represents Proposal 1's total charge for an order of x gifts.

(b) State a linear function g(x) that represents Proposal 2's total charge for an order of x gifts.

(c) If Thomas were to purchase 120 special gifts, as cheaply as possible. With which company should he place his order? Show work/explanation.

(d) For what number of gifts is the total charge exactly the same for both companies? Show algebraic work/explanation.

(e) What would be the payment if the level detected in (d) is to be purchased?

(f) Fill in the blanks:

Proposal 2 is the cheaper option if ________(choose less or more ) than ______ (enter number) gifts are ordered.

8) 5 points. Let . (no explanation required)

(a) State the zero(s) of the function. ________

(b) Which of the following is true? ______

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) 10 points. A graph of y = f (x) follows. No formula for f is given.

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

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

y = f (x)

2

4

-4

-2

-4

2

4

-2

GRAPH A (below) GRAPH B (below)

2

4

-4

-2

-4

2

4

-2

2

4

-4

-2

-4

2

4

-2

GRAPH C (below) GRAPH D (below)

2

4

-4

-2

-4

2

4

-2

22

44

-4-4

-2-2

-4-4

22

44

-2-2

10) 5 points. Write the equation IN SLOPE-INTERCEPT FORM for the line passing through the point (6, 8) which is perpendicular to the line shown below:

4x + 2y = –16