U7D9 Review Adding and Graphing Rational Equations May9

Graphing Rational Functions

Example:

Graph the following rational function and answer the following questions.

Horizontal Asymptote:

Compare the degree of the numerator (n) and the degree of the denominator (d).

If n < d, then H.A. at y = 0

If n = d, then H.A. at y = (lead coefficient/lead coefficient)

If n > d, then there is a slant asymptote

n = d

so the H.A. for f(x) is at y = 1.

Vertical Asymptote:

Occur when a number makes the denominator equal 0. These numbers would make the fraction undefined.

x + 2 = 0 when x = -2

so the V.A. for f(x) is at x = -2.

X-Intercept:

Any number that make the numerator equal 0 is an x-intercept.

x - 6 = 0, when x = 6

so x-intercept at (6,0)

Y-Intercept:

Y-intercepts occur at the result from plugging zero in for x.

so y-intercept at (0,-3)

Domain - All the possible x-values that can be used in the function.

Range - All possible results from the inputs.

Find the DOMAIN and RANGE for:

Solution:

Begin with the graph for the function.

In this graph, any number could be x (domain), except -2.

-2 makes the denominator zero, so it is not permitted.

Domain: All real numbers except -2

or

For the range, this graph shows our results could be any value except 1.

Range: All real numbers except 1

or