Download AII H Notes c6 s2 diff format

6.2 Evaluating and Graphing Polynomial Functions
Students will be able to:
Evaluate a polynomial function.
Graph a polynomial function.
Polynomial Function
f(x) =
where
, the exponents are all whole numbers and the
coefficients are all real numbers.
would be the leading coefficient,
is the constant, and n is the degree. A polynomial is written in
standard form if its terms are written in descending order of exponents
from left to right.
Degree
0
1
2
3
4
type
constant
linear
quadratic
cubic
quartic
Standard Form
Example 1 Identifying Polynomial Functions
Decide whether the function is a polynomial function. If it is, write it in standard
form and state its degree, type, and leading coefficient.
a. f(x) =
b. f(x) =
c. f(x) = 6
d. f(x) =
One way to evaluate a function is to use direct substitution.
If we look at the function, f(x) = 2x⁴ - 8x² + 5x – 7, and evaluate when x = 3.
f(3) = 2(3)⁴ - 8(3)² + 5(3) – 7
= 162 – 72 + 15 – 7
= 98
Another way to evaluate this is to use synthetic substitution.
Example 2 Use Synthetic Substitution
Use synthetic substitution to evaluate: f(x) = 2x⁴ - 8x² + 5x – 7, when x = 3.
Example 3 Evaluating a Polynomial Function in Real Life
The time t(in seconds) it takes a camera battery to recharge after flashing n times
can be modeled by t = 0.000015n³ - 0.0034n² + 0.25n + 5.3. Find the recharge
time after 100 flashes.
End behavior of functions.
Looking at a functions behavior as it goes to positive infinity(
infinity ( - ). The expression x
and negative
is read “x approaches positive infinity”.
Look at the end behavior for the following functions.
f(x) = x
f(x) = - x
f(x) = x²
f(x) = -x²
You try. Use a graphing calculator to investigate the end behavior for the
following function.
1. f(x) = x³
2. f(x) = - x³
3. f(x) = x⁴
4. f(x) = - x⁴