Polynomial Functions Assignment
DUE: Friday, February 14, 2014 BY 1:15pm
Class ID: ____ Name: _______________________________
Score:__________
Math 1080 – 001 Spring 2014
Instructor: Katrina Johnson
Complete the following exercises. No credit will be given without supporting work. This assignment will
be graded for correctness and you will receive a score out of 10. Print out these pages and include all
relevant work in the space provide. Staple the pages together and turn in at class on Friday. The
solutions will be posted on CANVAS.
1. Consider the polynomial function
f (x) = 6x 5 −13x 4 −13x 3 + 20x 2 +12x +16
a) What information does Descartes’ rule of signs give about the number of positive and negative real
zeros of f(x)?
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b) List the possible rational roots of f(x)?
x = ________________________________________________________
c) Show that x=3 is an upper bound of the zeros of f(x).
d) Show that x=-3 is a lower bound of the zeros for f(x).
e) Revise your list of possible rational roots given the information from parts c and d.
x = ________________________________________________________
f) Find all the zeros of f(x).
g) How does the conjugate pair theorem relate to your answer in part f.
h) What is the domain of f(x)? Explain your reasoning. Write your answer in interval notation.
Domain: _____________
i) Describe the end behavior of the function f(x).
j) What is the range of f(x)? Explain your reasoning. Write your answer in interval notation.
Range: _____________
k) What are the x-intercept(s) of f(x)? Write your answer(s) as points. How does this relate to your
answer in part f.
x-intercept(s): _____________________
l) What is the y-intercept of f(x)? Write you answer as a point.
y-intercept: _____________
m) True or False: The function f has an inverse. Explain your reasoning.
n) Sketch a graph of f(x). Make sure your graph is consistent with your work in the previous steps.
2. Consider the function
g(x) = 3x 3 + x 2 −10x − 8 . Note: This function is not a polynomial.
Find the domain of g. Write your answer in interval notation.
(The following parts should help you organize your work.)
a) What must be true of the polynomial
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p(x) = 3x 3 + x 2 −10x − 8 ? (Hint: Your answer should be a
nonlinear inequality.)
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b) Solve the nonlinear inequality.
i) Find the critical values.
ii) Sign Line.
c) What is the domain of g(x)? Write your answer in interval notation.
Domain: ____________________________________