### MATH 100 Quiz 4

**Name:**

You may use a calculator on this quiz. You may not use a cell
phone or computer. If you wish partial credit for incorrect answers,
please show your work carefully and give justifications for your
answers. If you find that you are spending a lot of time on one
problem, leave it blank and move on to the next. There are questions
on both sides of this page.

- (15 points; 1.6:3) Sketch the graph of the function g(x) =
(x-5)
^{2}. Hint: the graph takes the shape of a parabola.

- (15 points) Guess the equation of the function whose graph is shown below.

- (15 points; 1.7:2) Describe the domain of the rational function f(x) = 7/(x-5).

- (1.7:6) Suppose f(x) = 6x+7 and g(x) = x-1. Find:

a) (5 pts) (f-g)(x)

b) (10 pts) (f*g)(x)

- (20 points 1.7:7) If f(x)=3x
^{2}+x+4 and g(x)=2-x, find
f(g(x)).

- (15 points) Suppose f(x)=6x+7. Does the function f(x) have an
inverse? If not, explain why not. If so, find the inverse and check
your answer. (There are at least three different ways to check your
answer; you will lose 5 points if you do not show your work or explain
how you checked your answer.)

**Bonus** (5 points) Sketch the graph of the inverse of the
function shown in problem 2. (You may sketch it on the graph in
problem 2; if you do so, please make a note of that here.)