Question

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

5. \(\,f\left( {\bf{2}} \right) = {\bf{4}}\),\(\,f\left( { - {\bf{2}}} \right) = - {\bf{4}}\),\(\mathop {{\bf{lim}}}\limits_{x \to - \infty } \,\,f\left( x \right) = {\bf{0}}\), \(\mathop {{\bf{lim}}}\limits_{x \to \infty } \,f\left( x \right) = {\bf{2}}\)

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

As the value of the functionf is increasing from \( - 4\) to 4 at \(x = - 2\) to \(x = 2\).It shows that graph is increasing between these two points.

When x approaches\( - \infty \), the value of the functionf will approach to 0. Similarly, when x approaches to \(\infty \), the value of f will approach to 2.

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.