Question

Graph the following rational functions

Answer 1

Answer:

See attachment.

Step-by-step 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.

$3 {x}^{2} - 9 = 0$

${x}^{2} - 3 = 0$

$x = \pm \sqrt{3}$

$x = - \sqrt{3} \: or \: x = \sqrt{3}$

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

The y-intercept is

$y = \frac{2 \times 0 + 8}{3 {(0)}^{2} - 9 } = - \frac{8}{9}$

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.