Graphing Rational Functions Honors Algebra II Keeper

Step #1 Find the y-intercept by finding f(0).

Step #2 Find the x-intercept(s) by setting the numerator equal to zero and solving for x.

Step #3 Find the vertical asymptotes by setting the denominator equal to zero and solving for x.

Step #4 Find the horizontal asymptote.

If the degree of the numerator is… Bigger than the degree of the denominator, there is NO horizontal asymptote.

If the degree of the numerator is… Smaller than the degree of the denominator, y = 0 is the horizontal asymptote.

If the degree of the numerator is… the same as the degree of the denominator, Y =

Step #5 Find any slant asymptotes. If the degree of the numerator is exactly one degree larger than the denominator, there is a slant. Use long division to find it.

Step #6 Make a table of values. Choose x values on both sides of all vertical asymptotes.

Step #7 Substitute the x values back into the original problem to find the matching y values.

Step #8 Graph the intercepts. Graph the asymptotes using dotted lines. Graph the points from the t-chart.

Step #9 Connect the points using smooth curves.

Example

Example

Example

Example

Example

Example