Describing Transformations of Rational Functions

Let's start by recalling possible transformations of the parent function $f (x) = \frac{1}{x} .$

Function	Transformation of the Graph of $f (x) = \frac{1}{x}$
$g (x) = \frac{1}{x - h}$	Horizontal translation by $h$ units. If $h > 0,$ the translation is to the right. If $h < 0,$ the translation is to the left.

Now, let's consider the given function. $g (x) = \frac{1}{x + 3} \Leftrightarrow g (x) = \frac{1}{x - ( - 3 )}$ We can see that $h = - 3 .$ Therefore, the graph of $g (x)$ is a translation of the graph of $f (x)$ $3$ units left.

Describing Transformations of Rational Functions 1.7 - Solution