Chapter 2.4, Problem 157E

Sketch the graph of the function $y=f\left(x\right)$ with

properties i. through vii.

i.  The domain of f is $\left(-\infty ,+\infty \right)$ .

ii. f has an infinite discontinuity at x = -6.

iii. f(-6) = 3

iv.  $\underset{x\to -3^{-}}{\lim }f\left(x\right)=\underset{x\to -3^{+}}{\lim }f\left(x\right)=2$

v.  $f\left(-3\right)=3$

vi. f is left continuous but not right continuous at x = 3.

vii.  $\underset{x\to -\infty }{\lim }f\left(x\right)=-\infty$ and $\underset{x\to +\infty }{\lim }f\left(x\right)=+\infty$