Guidelines for Curve Sketching
y-intercept: set x=0 and evaluate y.
x-intercept: set y=0 and solve for x. (skip this step if the equation is difficult to solve)
for rational functions, vertical asymptotes can be located by equating the denominator to 0 after canceling any common factors.
to determine the right-end behavior;
to determine the left-end behavior.
for rational functions, slant asymptotes occur when the degree of the numerator is one more than the degree of the denominator.
find the critical numbers:
• use the First Derivative Test to find: intervals of increase/decrease
and local extrema.
• inflection points occur where the direction of concavity changes.
find possible inflection points by equating the
occur where the direction of concavity changes.