Question

Graph the following rational functions

Answer 1

See attachment.

Explanation:

We want to graph the rational function;

`y = \frac{2x + 8}{3 {x}^(2) - 9 }`

The vertical asymptotes occur at where the denominator is zero.

`3 {x}^(2) - 9 = 0`

`{x}^(2) - 3 = 0`

`x = \pm √(3)`

`x = - √(3) \: or \: x = √(3)`

The horizontal asymptote is y=0, since the degree of the numerator is less than the degree of the denominator.

The y-intercept is

`y = \frac{2 * 0 + 8}{3 {(0)}^(2) - 9 } = - (8)/(9)`

The x-intercept is

`0= \frac{2x + 8}{3 {x}^(2) - 9 }`

`2x + 8 = 0`

`x = - 4`

With this information we can graph the function as shown in attachment.