There are 190 points possible. The point value for each
problem is labelled next to the
problem number .
1. (3pts each) True or False:
(a) The point (1, 4) is on the graph of the function f where f(x) = 3x3 − 2x +
3.
(b) The lines 2y = −6x + 10 and y + 3x = 0 are parallel.
(c) The fol lowing could be a graph of a polynomial function of degree 3.
(d) The domain of the function g whose rule is
is [0,∞).
(e) If g(x) = −f(x) + 4, then the graph of g is the graph of f shifted down 4
units
and then reflected about the x-axis.
(f) If x2 −9 is a factor of a polynomial f(x), then x−3 and x + 3 are also
factors of
f(x).
(g) There is no real number x such that 
.
(h) For all x > 0
2. (3pts each) Fill in the blank.
(a) If f(x) = 3 log (x − 3) then f(4) = 
(b) If f is an even function and the point (1, 4) is on the graph of f, then
f(−1) =
(c) If f(x) = ln(x) and 
then the domain of
the function
is
(d) If f is a one-to-one function with domain (−2, 5)∪[2, 5] and range [1, 3),
then the
domain of f -1 is and the range of f
-1 is
(e) If f is a polynomial function and f(7) = 0, then we know
is a
factor of f(x).
3. (10pts) Give the equation of the line which passes through the points (0, 4)
and (9,−5).
4. (10pts) Solve for x
x 2 − 16 = 3x(x − 4)
5. (10pts) Find the center and radius of the circle which is the graph of the
following
equation.
x2 + 6y − 2 = 3 − y2
6. (10pts) Recall that the difference quotient for a function f is given by
Compute the difference quotient for f where
f(x) = 12x4 + log(x) − x2.
(You do NOT need to simplify your answer )
7. (10pts) Sketch a graph of the function g where
8. (10pts) If you invest $25 at 31% compounded
continuously , how long will it take for
you to have $137 ? (You do not need to simplify your answer, but be sure to
include
units)
9. (10pts) Use the Round Trip Theorem to show that the
functions g and f are inverses
where
g(x) = 2x + 4 and 
10. (10pts) Find the inverse of the one-to-one function f
where
11. (10pts) Recall that the area A of a triangle with base
b and height h is given by
. What is the maximal area of a triangle in
which the sum of the base and
twice the height is 4?
12. (3pts each) Let f be the rational function whose rule
is given by
(a) State the domain of f.
(b) State the horizontal asymptote of the graph of f.
(c) Find all vertical asymptotes of the graph of f (if any exist).
(d) Find all x-values of holes in the graph of f (if any exist).
(e) Give the (x, y)-coordinates of all the holes of the the graph of f (if the
graph has
any holes).
(f) Find the y- intercept of the graph of f (if one exists).
(g) Find the x-intercept(s) of the graph of f (if any exist).
13. (10pts) Use long division to find all the roots of
f (x) = x3 + x2 − 14x − 24 given that
f(−3) = 0.
14. (10pts) For what values of x is |3x − 11| > 7 ? Give
your answer in interval notation.
15. (10pts) Is the function f whose rule is given by f(x)
= 2x2 −4x even, odd, or neither?
(You must justify your answer to receive credit)
16. (10pts) Solve for x
