Worksheet 3.2 - University of South Alabama

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MA112
Section 106
Dr. Byrne
Fall 2009
Worksheet:
Homework Problems Section 3.2
1. Match the equation with the graph.
a. y  xx  2 x  2
2
b. y  xx  2x  2
______
2
______
c. y  xx  2x  2
d. y  x 2 x  2x  2
______
______
2. Match the equation with the graph.
a. y  x  1x  1x  3
______
b. y  x 2 x  2
______
c. y  x  2x  1
2
d. y  xx  21  x 
______
______
Determine the lowest possible degree for the polynomial whose graph is shown.
______
______
______
______
Carefully graph the function using a t-table.
Graph f ( x)  x 3 .
x
y
Graph f ( x)  x 4 .
x
y
Roughly sketch the graphs of the functions below using the graphs for f ( x)  x 3 and f ( x)  x 4 .
7. f ( x)  3x 3  2 .
9. f ( x)  ( x  3) 4  2 .
11. f ( x)   1
2
x  33  3 .
Use the zeros and the end behavior of the polynomial function to roughly sketch the graph.
13. f ( x)  x  2x  2x  3 15. f ( x)  xx  1x  1x  2 16. f ( x)   xx  1x  2x  3
Use the zeros and the end behavior of the polynomial function to roughly sketch the graph.
17. f ( x)   x 3 x  2
19. f ( x)   x 2 x  1
2
21. f ( x)  x 3  x 2  2 x
Roughly sketch the curve by shifting the graph of f (x) .
23. y  f ( x  2)
24. y  f ( x  1)
27. y  f ( x)
29. y  f ( x)  1
f (x )
25. y  f ( x  2) +1
31.
a. Sketch the graph of a polynomial P (x ) that has
zeros of multiplicity 1 at x  1 , x  1 and
x  2 and that satisfies P(x)   as x   and
P(x)   as x   .
b. What is the least possible degree of this
polynomial?
32.
a. Sketch the graph of a polynomial P (x ) that has
zeros of multiplicity 1 at x  0 , x  1, has a zero
of multiplicity 3 at x  3 and that satisfies
P(x)   as x   and
P(x)   as x   .
b. What is the least possible degree of this
polynomial?
37. Determine the polynomial of degree 4 whose graph
is shown in the figure.
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