Question

In Exercises 21–24, sketch the graph of a function f that has the listed characteristics.
$$\begin{gathered} f(-1)=2; \\ f\text{'}(-1)=3; \\ f\left(1\right)=-2; \\ f\text{'}\left(1\right)=3 \end{gathered}$$

Short answer

The graph of the function with the given characteristics is:

Step-by-step solution

Step 1. Given Information.

The characteristics of the function:

$$\begin{gathered} f(-1)=2; \\ f\text{'}(-1)=3; \\ f\left(1\right)=-2; \\ f\text{'}\left(1\right)=3 \end{gathered}$$

Step 2. Observe from the given information.

From the given information we can conclude that the function has a bend at $x=-1,x=-3,x=2$

Step 3. Graph the function.

Graph the function.