1. Graphing Polynomial Functions
Find all roots (zeroes) by factoring if possible.
Check “intermediate” values to see behavior of the graph.
Use “leading coefficient” test to check end behavior of the graph.
Plug a large negative number to check left-end behavior
Plug a large positive number in to check right-end behavior.

2. Graphing Polynomial Functions
Practice Examples:
f(x) = -x3 + 4x
f(x) = (x+1)4
f(x) = x4 – 5x2 + 4
f(x) = x5 - x

3. Graphing Rational Functions
Must contain a denominator
Any undefined values will be vertical asymptotes.
To find horizontal asymptotes, use the following rules:
Divide highest power of numerator by highest power of denominator.
Take resulting rational quotient and plug in large negative and large positive x value.
Horizontal Asymptote will be a number, +∞, or -∞, or 0
Set equation equal to 0 to solve for roots.
Follow same procedure for finding “intermediate” values

4. Graphing Rational Functions
f(x) = 2x + 1
x + 1
2. f(x) = 2x2
x2 – 1
f(x) = x2
x2 – x - 2