Which is not an asymptote of the function A.x = –4 B.x = 7 C.x = 4 D.f(x) = 0

8.4 – Graphing Rational Functions

General Rational Functions In this section we are going to learn to graph rational functions for which p(x) and q(x) are higher-degree polynomials. Graph by finding the following: Vertical Asymptote(s), if any: Set the denominator = 0 and solve. x and y intercepts: set opp. variable equal to 0 You can always find critical points on graph as well (maximums, minimums, etc.)

Horizontal Asymptote(s), if any. Compare the degree of the numerator (m) to the degree of the denominator (n). m < n: HA is y = 0 m = n: HA is Leading coefficient of the numerator / LC of the denominator m > n: HA does not exist

Example 1: Graph the function, then state the domain and range and any asymptote equations. a)

b)

c)

Example 2a: Graph Oblique Asymptotes Graph

Ex 2 continued.

Example 2b)

Example 2c) Graph

Example 3: Graph with a point of discontinuity Graph.

Which graph below is the graph of ? A.B. C.D.

Application A boat traveled upstream at r 1 miles per hour. During the return trip to its original starting point, the boat traveled at r 2 miles per hour. The average speed for the entire trip R is given by the formula Draw the graph if r 2 = 15 miles per hour.

Application Answer Simplify. Original equation r 2 = 15