Question

Graph all vertical and horizontal asymptotes of the function
f(x)= -8x-13/2x-1

Answer 1

To find the vertical asymptote, set the denominator equal to zero and solve for the variable x using algebra. The denominator is 2x-1 so if you set that equal to zero that would be 2x-1=0 ⇒ 2x=1 ⇒
`x= (1)/(2)` is the vertical asymptote

To find the horizontal asymptote, there are three possibilities. Look at the degree of the numerator and denominator. Compare the degrees using the rules attached. Notice both the denominator and numerator have the same degree, so using the rule, the horizontal asymptote would be
`y= (a)/(b)` or in this case a=-8 and b=2 so the vertical asymptote is
`y= (-8)/(2)` or y=-4

Hope this helps

Answer 2

Refer the attached figure below.

Explanation:

Given : Function
`f(x)=(-8x-13)/(2x-1)`

To find : Graph all vertical and horizontal asymptotes of the function ?

Solution :

To find the vertical asymptote put the denominator of the function equal to zero.

The value of x from denominator is the vertical asymptote.

`f(x)=(-8x-13)/(2x-1)`

Denominator =0

`2x-1=0`

`2x=1`

`x=(1)/(2)`

So, The vertical asymptote is
`x=(1)/(2)`

To find the horizontal asymptote we determine the degree of numerator and denominator.

Deg(num)=Deg(den)

So,
`y=\frac{\text{leading coefficient of nr.}}{\text{leading coefficient of dr.}}`

`y=(-8)/(2)`

`y=-4`

So, The horizontal asymptote is
`y=-4`

Refer the attached figure below.