Example 2
Completion requirements
| Example 2 |
Multimedia |
Use the graph of \(y = (x - 3)^2 - 4\) to sketch the graph of \(y = \frac{1}{(x - 3)^2 - 4}\).
Sketch the graph of \(y = (x - 3)^2 - 4\).
Plot the points where \(y = \pm 1\). This is where the two functions will intersect.
Use the points of intersection and the asymptotes to sketch \(y = \frac{1}{(x - 3)^2 - 4}\).
The vertical asymptotes of the graph of \(y = \frac{1}{(x - 3)^2 - 4}\) pass through the \(x\)-intercepts of the graph of \(y = (x - 3)^2 - 4\). The reciprocal function is of the form \(y = \frac{1}{f(x)}\), so \(y = 0\) is the horizontal asymptote. Draw these asymptotes on the grid.
Plot the points where \(y = \pm 1\). This is where the two functions will intersect.
Use the points of intersection and the asymptotes to sketch \(y = \frac{1}{(x - 3)^2 - 4}\).