# Can you cross a slant asymptote?

**cross a slant**or horizontal

**asymptote**. This is not the case! A graph

**CAN cross slant**and horizontal

**asymptotes**(sometimes more than once). It's those vertical

**asymptote**critters that a graph cannot

**cross**.

Correspondingly, can you cross an asymptote?

Whereas **you can** never touch a vertical **asymptote**, **you can** (and often **do**) touch and even **cross** horizontal **asymptotes**. Whereas vertical **asymptotes** indicate very specific behavior (on the graph), usually close to the origin, horizontal **asymptotes** indicate general behavior, usually far off to the sides of the graph.

**You**may

**have**0 or 1

**slant asymptote**, but no more than that. A graph

**can have**both a vertical and a

**slant asymptote**, but it CANNOT

**have**both a

**horizontal and slant asymptote**.

**You**draw a

**slant asymptote**on the graph by putting a dashed

**horizontal**(left and right) line going through y = mx + b.

Correspondingly, how do you find the crossing point of a slant asymptote?

Your **oblique asymptote** equation is correct, but your work is wrong. You should get x=1 as your x coordinate for the **point** of **intersection**. To **find the** y coordinate, simply plug in x=1 to either equation and you'll **see** that the **point** of **intersection** is (1,0).

**If** the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the **horizontal asymptote**. **If** the polynomial in the numerator is a higher degree than the denominator, **there** is no **horizontal asymptote**.