Chapter 1.1, Problem 26ES

Sketch a possible graph for a function $f$ with the specified properties. (Many different solutions are possible.)

(i) $f\left(-1\right)=0,f\left(0\right)=1,f\left(1\right)=0$

(ii) $\underset{x\to -1^{-}}{\lim }f\left(x\right)=0$ and $\underset{x\to -1^{+}}{\lim }f\left(x\right)=+\infty$

(iii) $\underset{x\to 1^{-}}{\lim }f\left(x\right)=1$ and $\underset{x\to 1^{+}}{\lim }f\left(x\right)=+\infty$