Graphing Rational Function with a Hole
Example 2
We are now going to analyze and graph a rational function that has a hole.
Graph of Rational Function - Example 2
The graph of the rational function is attached below. Compare the graph to the above analysis.
Intervals
~ (-∞, -2) region is positive, therefore, the graph is above the x-axis and "hugs" the vertical asymptote at x = -2.
Notice the graph does NOT cross the x-axis.
It "hugs" the horizontal asymptote y = 2.
~ (-2, ½) region is negative, therefore, the graph is below the x-axis and "hugs" the vertical asymptote, x = -2.
~ (½, ∞) region is positive, therefore, the graph is above the x-axis and "hugs" the horizontal asymptote at y = 2.
This graph will cross the x-axis because of the zero at x = ½.