Chapter 2.7, Problem 41E

Sketch the graph of a function $g$ that is continuous on its domain $(-5,5)$ and where $g(0)=1,g\prime (0)=1,g\prime (-2)=0$ , $\underset{x\to -5^{+}}{\lim }g(x)=\infty$ , and $\underset{x\to 5^{-}}{\lim }g(x)=3$ .