LT 7.01 I can graph a polynomial of degree 3 or higher using end behavior and
intercepts
LT 7.05 I can graph a polynomial on a calculator and be able to indentify: degree,
number of turns, and the multiplicity of zeros.
Adv Alg
Unit 7 Graph Behavior
Name:
1/10/13
Consider end behavior and the number of turns each function will take and match the following
functions with their graph below. Try this exercise without your graphing calculator.
1)
f ( x )  x 3  4x 2
2)
f (x )  x 6  9x 4
3)
f (x )  6x  3x 2  3
4)
f (x )  1  x  x 3
5)
f (x )  2  3x 3  x 5
6)
f (x )  5  x 4  x
A)
B)
C)
D)
E)
F)
Use your graphing calculator to create an accurate sketch of the following curves. Indicate zeros
and y-intercept values with three decimal points of accuracy.
7)
f (x )  x 4  2x 3  5
8)
f (x )  x 2  10x  x 5
Based upon the leading term, consider the end behavior of the following polynomials. Choose the
most appropriate description.
9)
f (x )  9  2x 2  3x 4
10)
f (x )  x  3x  4x
4
5
2
A)
Starts positive, Ends positive
B)
Starts negative, Ends negative
C)
Starts positive, Ends negative
D)
Starts negative, Ends positive
Given the following factored polynomials, determine the zeros. Indicate the multiplicity of each
root. Using the zeros, multiplicity and end behavior, sketch a quick graph of the curve.
12)
f (x )  (x  3)(x  3)(x  1)2
13)
f (x )  x 2 (x  4)3 (x  5)