Chapter 4.4, Problem 67AYU

Challenge Problem Removing a Discontinuity In Example $5$

we graphed the rational function $R\left(x\right)=\frac{2x^2-5x+2}{x^2-4}$

and found that the graph has a hole at the point $\left(2,\frac{3}{4}\right)$. Therefore, the graph of $R$ is discontinuous at $\left(2,\frac{3}{4}\right)$. We can remove this discontinuity by defining the rational function $R$ using the following piecewise-defined function:

$R\left(x\right)=\{\begin{array}{l}\frac{2x^2-5x+2}{x^2-4}\text{if }x\ne \text{2}\\ \frac{3}{4}\text{if }x=2\end{array}$

Redefine $R$ from Problem $33$ so that the discontinuity at $x=3$ is removed.

Redefine $R$ from Problem $33$ so that the discontinuity at $x=\frac{3}{2}$ is removed.

$R(x)=\frac{x^2+x-12}{x^2-x-6}$