Chapter 2.4, Problem 158E

Sketch the graph of the function $y=f\left(x\right)$ with properties i. through iv.

i. The domain of f is [0, 5].

ii.  $\underset{x\to 1^{+}}{\lim }f\left(x\right)$ and $\underset{x\to 1^{-}}{\lim }f\left(x\right)$ exist and are equal.

iii.  f(x) is left continuous but not continuous at x = 2, and right continuous but not continuous at

x= 3.

f(x) has a removable discontinuity at x = 1, a jump discontinuity at x = 2, and the following limits hold: $\underset{x\to 3^{-}}{\lim }f\left(x\right)=-\infty$ and $\underset{x\to 3^{+}}{\lim }f\left(x\right)=2$ .