Return to Assignments Fractional functions and graphs
Assignment 7
Given the function:
Find:
the vertical asymptote;
the horizontal asymptote;
the intersection point with the -as if it exists;
the intersection point with the -as if it exists.
Based on these results sketch the result in the figure.
Solution
The line seems to be an asymptote. However, when we substitute this value in the formula we get
. That the numerator yields
for
means that the numerator contains the factor
. Indeed, the numerator can be factorized:
. Now the function can be rewritten:
if
.
We do not need to do complicated calculations any more. There also no asymptotes. The graph of the function is equal to the graph of , excluded the point
. The graph approaches
if
approaches
The graph in the figure is valid, exluded the point
.