Unit 3 – Polynomial Function
REVIEW
1)
Determine if each binomial is a factor of the function f(x) = x4 – 2x3 + 4x2 –
a) Is x + 1 a factor?
b) Is x – 7 a factor?
c) Is x + 7 a factor?
d) Is x – 3 a factor?
2)
Determine the number of positive and negative real roots each function below has.
a) f(x) = x4 - 2x2 + 1
b) f(x) = 2x3 - 3x2 + x – 1
c) f(x) = x4 + x3 + 2x2 - x – 3
3)
List all the POSSIBLE roots of the function f(x) = x3 + 3x2 – 5x + 10
4)
Find all the zeros of f(x) = 2x3 - 4x2 + 5x – 3
14x – 21 .
5)
Identify each of the following for the graph to the right.
a) Domain
b) Range
c) End Behavior
d) Zeros
e) Y-intercept
f) Intervals of increase
g) Intervals of decrease
h) Label Max/ Min (on graph)
6)
Determine the end behavior of each function. Write in statement form (As x  …)
a) f(x) = -3x3 + 2x2 – 5x + 7
b) f(x) = 3x4 + 6x2 + 5
c) f(x) = 2x3 + 4x2 +3x + 8
7)
Make a sketch of each function.
a) f(x) = (x + 1) (x – 2)2
b) f(x) = (x + 3)2 (x – 1)3
c) f(x) = -4x2 (x + 2) (x – 3)
8)
Divide.
a)
b)
c)
x3  13x 2  39x  20 x  9
x3  12x  20 x  2
5x3  3x 2  5x  3 x  1