Graph Intercepts Extrema Inflection Points and Asymptotes

This objective combines several previous objectives. To review:

Intercepts

To find the y intercept, plug 0 in for x.

To find the x intercepts, find the zeroes of the function.

Extrema

These are the relative maxima and minima of the function.

Find the extrema by finding the zeroes of the first derivative of the function.

Determine if each is a max or min by making a sign chart and testing values on either side.

Inflection Points

Inflection points are where the direction of concavity changes.

Find the inflection points by finding the zeroes of the second derivative of the function.

Asymptotes

Asymptotes are the lines (horizontal, vertical, or oblique) where branches of the function approach but never reach.

Find vertical asymptotes by looking for the zeroes of the denominator in rational functions.

Find horizontal or oblique asymptotes by comparing the degree of the numerator and denominator in rational functions.