CPM Homework Help : PC Problem 5-73

Sketch the graph of $f ( x ) = - \frac { 1 } { x - 3 } + 2$ , then evaluate $\lim \limits _ { x \rightarrow- \infty } f ( x )$ .

Hint 1:

The parent graph of $f(x)$ is $y = \frac{1}{x}$ .

What does that graph look like?

Graph:

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

Decreasing rational function, asymptotes as the axes, left curve below & left of origin, right curve above & right of origin.

Hint 2:

What does a negative sign do to a graph?
What about $\left(x − 3\right)$ and $+2$ ?

Show transformed graph:

Increasing rational function, asymptotes at x = 3 & y = 2, left piece above & left of asymptote intersection, right piece below & right of asymptote intersection.

Use the graph to evaluate the limit.