At which values of x does the function F(x) have a vertical asymptote? Check all that apply, F(x) 9 (x - 1)(x-8)

Question

asked Aug 11, 2021 203k views

2 Answers

Ashley Baldry · Answer 1 · 2021-08-15T16:55:52+0000

Answer:

The values of x that makes f(x) have a valid asymptote are 1 and 8

Explanation:

Given

f(x) = (9)/((x-1)(x-8))

Required

At what value does f(x) has a vertical asymptote

To solve this, we simply equate the denominator of f(x) to 0;

This is done as follows

{(x-1)(x-8)} = 0

This can be split to

${(x-1) = 0 \ or\ (x-8)} = 0$

Remove brackets

$x-1 = 0 \ or\ x-8 = 0$

Make x the subject of formula in both cases

$x-1+1 = 0+1 \ or\ x-8+8 = 0+8$

$x= 0+1 \ or\ x = 0+8$

$x= 1 \ or\ x = 8$

The values of x that makes f(x) have a valid asymptote are 1 and 8