The function is .

This function represents a transformation of the graph of .

The transformation of function general form is .

Thus, here

, the graph is stretches vertically and reflected across the -axis.

, the graph is shifted units left.

, the graph is translated units down.

**Graph:**

Graph the function .

Observe the graph:

Domain is .

Range is .

**Identify the asymptotes.**

Identify the -values for is undefined.

is not defined for value of .

Thus, there is an asymptote at .

From , as a -values decrease, -values approach , and as -values increase, -values approach .

Thus there is an asymptote at .

Graph of the function is

The domain is and the range is .

The asymptote at .

"I want to tell you that our students did well on the math exam and showed a marked improvement that, in my estimation, reflected the professional development the faculty received from you. THANK YOU!!!" June Barnett |

"Your site is amazing! It helped me get through Algebra." Charles |

"My daughter uses it to supplement her Algebra 1 school work. She finds it very helpful." Dan Pease |