Question

In Problems 31– 42, graph each rational function using transformations.

$H\left(x\right)=\frac{-2}{(x+1)}$

Short answer

The graph of the function $H\left(x\right)=\frac{-2}{(x+1)}$is:

Step-by-step solution

Step 1. Given

The function$H\left(x\right)=\frac{-2}{(x+1)}$

To graph the function.

Step 2. Graph the parent function

Graph the basic function $y=\frac{1}{x}$

Step 3. Graph the function by shifting.

Replace $y=\frac{1}{x}$by

$y=\frac{1}{x+1}$, so that the graph shift horizontally left to one unit.

Step 4. Replace y=1x+1 by y=-2x+1

Replace $y=\frac{1}{x+1}$by

$y=\frac{-2}{x+1}$so that the graph stretched by the factor $2$and reflected about $x-$axis.