Question

I chose x=3 , x=-4 which was wrong the correct answer is x=1 , x=-2

can someone please explain how to get that answer

Answer 1

vertical asymptotes is x = -2 and x = 1

Explanation:

For rational functions, the vertical asymptotes are the undefined points, also known as the zeros of the denominator (below the line), of the simplified function.

This means
`-4x^(2) - 4x + 8` is equal to zero than solve

*image below*

Hope it helps :)

Let me know if you have any questions or anymore help lmk, happy to help with any school work!!

Answer 2

We are give with the function:

`{\quad \qquad \longrightarrow f(x)=(x^(2)+x-12)/(-4x^(2)-4x+8)}`

Vertical asymptotes are the points, where the function is not defined, so the denominator must be equal to 0 for making f(x) not defined

`{:\implies \quad \sf -4x^(2)-4x+8=0}`

Dividing both sides by -4, we have;

`{:\implies \quad \sf x^(2)+x-2=0}`

Can be further written as:

`{:\implies \quad \sf x^(2)-x+2x-2=0}`

`{:\implies \quad \sf x(x-1)+2(x-1)=0}`

`{:\implies \quad \sf (x-1)(x+2)=0}`

Using zero product rule, Equating both multiplicants to 0, we have:

`{:\implies \quad \boxed{\bf{x=1\quad or\quad -2}}}`

This is the required answer