http://www.ck12.org Chapter 1. Functions and Graphs
Solution:
There is a vertical asymptote atx=0. The end behavior of the right and left side of this function does not match. The
horizontal asymptote asxapproaches negative infinity isy=0 and the horizontal asymptote asxapproaches positive
infinity isy=4. At this point you can only estimate these heights because you were not given the function or the
tools to find these values analytically.
Concept Problem Revisited
Asymptotes written by hand are usually identified with dotted lines next to the function that indicate how the function
will behave outside the viewing window. The equations of these vertical and horizontal dotted lines are of the form
x= andy=. When problems ask you to find the asymptotes of a function, they are asking for the
equations of these horizontal and vertical lines.
Vocabulary
Anasymptoteis a line that a function gets arbitrarily close to. The function may touch horizontal asymptotes, but
never touch vertical asymptotes.
Apiecewise functionis a function defined to be part one function and part another function.
Guided Practice
- Identify the horizontal and vertical asymptotes of the following function.
- Identify the horizontal and vertical asymptotes of the following function.
- Identify the horizontal and vertical asymptotes of the following piecewise function:
f(x) ={
ex− 1 x≤ 0
sinx 0 <x