Pre-Calculus Graphing Rational Expressions
Step 1: Graph R using your graphing utility. Step 2: Determine the domain. Step 3: Reduce the rational expression if possible.
Step 4: Determine the vertical asymptotes. Step 5: Decide if it has horizontal or slant asymptotes or perhaps neither. If it does, determine what they are. Step 6: Find intercepts. Step 7: Hand graph R.
Domain: All real except for zeros of the denominator. Vertical Asymptotes: Vertical lines that act as boundaries for our graph. These are the zeros of the denominator after the rational expression has been reduced. Horizontal Asymptotes: Depends on the degrees of the numerator and denominator. a. If the degree on top is less than the degree on bottom, the rational function is considered proper. y = 0 is the horizontal asymptote
Horizontal Asymptotes: b. If the degree on top equals the degree on bottom, then the horizontal asymptote is y = a/b where a and b are the lead coefficients. c. If the degree on top is exactly one more than the degree on the bottom, then you do not have a horizontal asymptote, you have a slant asymptote instead. d. If the degree on top is more than one more than the degree on the bottom, then you do have a horizontal or slant asymptote.
Slant asymptote: If the degree on top is exactly one more than the degree on the bottom, then you have a slant asymptote. Find the slant asymptote by dividing the numerator by the denominator and disregard any remainder.
1. R x
x 1 x x 4
Step 1: Graph using graphing calculator.
1. R x
x 1 x x 4
Step 2: Domain The domain is all Real except for o and –4.
Step 3: Reduce – done. Step 4: Vertical Asymptotes x = 0 and x = –4
Step 5: Horizontal Asymptote Degree numerator (DN) = 1 Degree denominator (DD) = 2 DN < D D This makes this a proper rational expression. y = 0 is the horizontal asymptote Step 6: Find x and y intercepts by either setting x or y equal to 0. x 1 0 1 x-intercept 0 y-intercept y x x 4 0 0 4 (â&#x20AC;&#x201C;1, 0) none 0 x 1 y is undefined x 1
Step 7: Hand graph
Step 7: Hand graph