# Functions, Graphs, and Limits

### Example 1

For the function find any horizontal, slant, or curvilinear asymptotes. Specify the type of each asymptote, and whether the function *f* approaches the asymptote as *x* approaches ∞, -∞, or both.

*f*(*x*) = 2^{-x}

### Example 2

For the function find any horizontal, slant, or curvilinear asymptotes. Specify the type of each asymptote, and whether the function *f* approaches the asymptote as *x* approaches ∞, -∞, or both.

### Example 3

For the function find any horizontal, slant, or curvilinear asymptotes. Specify the type of each asymptote, and whether the function *f* approaches the asymptote as *x* approaches ∞, -∞, or both.

*f*(*x*) = 3 + e^{x}

### Example 4

*f* approaches the asymptote as *x* approaches ∞, -∞, or both.

### Example 5

*f* approaches the asymptote as *x* approaches ∞, -∞, or both.

### Example 6

Find the horizontal / slant / curvilinear asymptote for the rational function.

### Example 7

Find the horizontal / slant / curvilinear asymptote for the rational function.

### Example 8

Find the horizontal / slant / curvilinear asymptote for the rational function.

### Example 9

Find the horizontal / slant / curvilinear asymptote for the rational function.

### Example 10

Find the horizontal / slant / curvilinear asymptote for the rational function.