HONOR CODE: On my honor, I have neither given nor received any aid on this examination.
Signature:
SHOW ALL WORK ON THIS EXAM!!!
1. Let: π(π₯) = β|5π₯ β 2| and π(π₯) = β3
a) SOLVE for x:
f (x) = g(x)
. What information about the graphs of these functions does the
solution give us?
b) SOLVE the inequality:
f (x) ο³ g(x)
c) Graph the two functions on the same coordinate plane. Does the graph back up your solution from
part (b)?
2. Sketch the graph: π(π₯) = (π₯ β 2)
2
(π₯ + 1)(π₯ + 2)
3
3. a) Let π(π₯) = π₯
4 β π₯
3 + 7π₯
2 β 9π₯ β 18 and
( ) 9
2
g x = x + . Use long division to show that g is a
factor of f. Explain.
b) Use the result found above to find all of the zeros (real and complex) of the polynomial f.
4. Let π(π₯) = 4π₯
4 + 5π₯
3 + 9π₯
2 + 10π₯ + 2.
a) List all of the possible rational zeros.
b) Use the division to factor the polynomial
f (x)
completely. HINT: -1/4 is a zero of f .
c) Find all of the zeros of
f (x)
and state the multiplicity of each zero.
5. Let the function f be defined as follows:
π(π₯) =
π₯
π₯
2 β 4
a) What is the domain of f ?
b) Does the graph of f have any vertical asymptotes? If so, find them.
c) Does the graph of f have any horizontal asymptotes? If so, find them.
d) Where will the graph of f intercept the x-axis?
e) Where will the graph of f intercept the y-axis?
f) Sketch the graph of f.
6.) (Bonus Problem) Graph the function:
π
(
π₯
)
=
π₯
2
β
5
π₯
+
4
π₯
2
β
2
π₯
+
1