Math Exercises

Show work/explanation where indicated. Answers without any work may earn little, if any, credit.

1. (6 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? ____

 

2. (6 pts) Let f(x)=|6-x|. (no explanation required)

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

(b) Which of the following is true? 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. (6 pts) Which of the following equations does the graph represent? Show work or explanation. 3. ______

 

A. y=- 2/3 x+4

 

B. y=- 3/2 x+4

 

C. y= 2/3 x+4

 

D. y= 3/2 x-6

 

4. (12 pts) Consider the points(– 4, – 3) and (2, 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), eitherdrawing it on the grid in the previous problem #3, or generating the graph electronically and attaching it.
(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. (8 pts) The amount of gas g in gallons in a car’s gas tank t days after a fill-up is modeled by g(t) = –0.5t2– 1.5t + 36 for 0 t6.
Find and interpret the average rate of change of gover the interval [0, 6].Show work.

 

6. (20 pts) Lauren wants to purchase custom-made bumper stickers to advertise her business. Two websites offer different deals:
Website A: Pay a fee of $80.00, plus $0.35 per bumper sticker
or Website B: Pay a fee of $49.25, plus $0.50 per bumper sticker

 

(a) State a linear function f (x) that represents Website A’s total charge for an order of x bumper stickers.

 

(b) State a linear function g(x) that represents Website B’s total charge for an order of x bumper stickers.

 

(c) Lauren wants to purchase 320 custom-made bumper stickers, as cheaply as possible. At which website should she place her order? Show work/explanation.

(d) For what number of bumper stickers is the total charge exactly the same at both websites? Show algebraic work/explanation.

 

(e) Fill in the blanks:
Website B is the cheaper option if ________(choose lessor more) than______ (enter number) bumper stickers are ordered.
7. (8 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 ?
EXPLAIN YOUR CHOICE.(Grid supplied for scratch work; You are NOT required to submit your own graph)

 

y = f (x)

GRAPH A (below) GRAPH B(below)

 

GRAPH C(below) GRAPH D(below)

 

8. (20 pts, no explanation required)
Consider the graph of the piecewise function y = f (x) pictured below.

State the value of f (2).

 

(b) State the x-intercept(s), if any.

 

(c) State the y-intercept(s), if any.

 

(d) State the domain of the piecewise function.

 

(e) State the range of the piecewise function.

 

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

 

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