Horizontal asymptote
Intros
Lessons
- Introduction to Horizontal Asymptote • Horizontal Asymptotes define the right-end and left-end behaviors on the graph of a function. • 3 cases of horizontal asymptotes in a nutshell…
Examples
Lessons
- Algebraic Analysis on Horizontal Asymptotes
Let's take an in-depth look at the reasoning behind each case of horizontal asymptotes:
- Case 1:
if: degree of numerator < degree of denominator
then: horizontal asymptote: y = 0 (x-axis)
→ horizontal asymptote:
- Case 2:
if: degree of numerator = degree of denominator
then: horizontal asymptote: y =
→ horizontal asymptote:
- Case 3:
if: degree of numerator > degree of denominator
then: horizontal asymptote: NONE
→
- Case 1:
- Graphing Rational Functions
Sketch each rational function by determining:
i) vertical asymptote.
ii) horizontal asymptotes
- Identifying Characteristics of Rational Functions
Without sketching the graph, determine the following features for each rational function:
i) point of discontinuity
ii) vertical asymptote
iii) horizontal asymptote
iv) slant asymptote