Question

Determine the vertical asymptote for the rational function f of x equals quantity x minus 4 end quantity divided by quantity 3 times x plus 2 end quantity.

(Worth 3 points)

x = −4

x equals negative two thirds

x equals two thirds

x = 4

Answer 1

yes, x = -2/3 is correct

Answer 2

vertical asymotote at
`x=(-2)/(3)`

Explanation:

`f(x)= (x-4)/(3x+2)`

vertical asymptote is the line where the graph goes close to the line but does not cross it.

To find vertical asymptote, we set the denominator =0 and solve for x

denominator is 3x+2

set 3x+2=0

Subtract 2 on both sides

`3x=-2`

divide both sides by 3

`x=(-2)/(3)`

vertical asymotote at
`x=(-2)/(3)`