Question

5-10 Sketch the graph of an example of a function f that satisfies all of the given conditions.

\(\,\mathop {{\bf{lim}}}\limits_{x \to - \infty } f\left( x \right) = - \infty \),\(\mathop {{\bf{lim}}}\limits_{x \to - {{\bf{2}}^ - }} f\left( x \right) = \infty \),\(\mathop {{\bf{lim}}}\limits_{x \to - {{\bf{2}}^ + }} f\left( x \right) = - \infty \), \(\mathop {{\bf{lim}}}\limits_{x \to {\bf{2}}} \,f\left( x \right) = \infty \), \(\mathop {{\bf{lim}}}\limits_{x \to \infty } \,\,f\left( x \right) = \infty \)

Short answer

The graph of an example of a function f is shown below:

Step-by-step solution

Step 1:Check the nature of the graph from the given values

It appears from the given value that there should be only twovertical asymptotes\(x = - 2\) and \(x = 2\).

So, the graph will be drawn in three sections for the asymptotes.

Sketch the graph of \(f\left( x \right)\)

The graph of an example of a function f is shown below:

Thus, the graph is obtained.