### Home > PC3 > Chapter 12 > Lesson 12.2.1 > Problem12-105

12-105.

My mystery function, f, has all of the following attributes:

• $\lim\limits_{ x \rightarrow \infty } f ( x ) = 6$

• $\lim\limits_{ x \rightarrow - \infty } f ( x ) = −3$

• $\lim\limits_{ x \rightarrow 8 ^ { + } } f ( x )$ does not exist, but $f(x)$ approaches negative infinity.

• $\lim\limits_ { x \rightarrow 8 ^ { - } } f ( x )$ does not exist, but $f(x)$ approaches positive infinity.

1. What, if anything, can you conclude about the asymptotes of the graph?

If $x$ approaches $±∞$, you are moving right/left on the graph.
What type of asymptote is this?

If the function is approaching $±∞$, your are moving up/down on the graph.
What type of asymptote is this?

2. Sketch a possible graph having these attributes.