Question

Determine the vertical asymptote for the rational function F of X equals quantity X minus end quantity divided by quantity2 times X plus 3 end quantity

Answer 1

We have been given a function
`f(x)=(x-4)/(2x+3)`. We are asked to find the vertical asymptote of the given rational function.

We know that vertical asymptote of a rational function is the point, where denominator of rational function is equal to zero.

To find vertical asymptote for our given rational function, we will equate denominator with 0 as:

`2x+3=0`

Let us solve for x.

`2x+3-3=0-3`

`2x=-3`

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

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

Therefore, the vertical symptote of our given rational function is
`x=-(3)/(2)`.