Question

At what value of x does the graph of the following function f(x) have a vertical asymptote? check all that apply. f(x)=1/(x-4)(x+1)

a. 4
b. 0
c. -1
d. 1
e. -4
f. 2

Answer 1

At values 4 and -1, the function F(x) has a vertical asymptote

Answer 2

Answer:4,-1

Explanation:

A function
`f(x)` is said to have vertical asymptote at a point
`x_(0)` if
`f(x_(0))` tends to infinity or negative infinity.

Given function is
`f(x)=(1)/((x-4)(x+1))`

When
`x=4`,

`f(x)=(1)/((4-4)(4+1))=(1)/(0)`

`f(4)`→∞

So,
`f(x)` has a vertical asymptote at
`4`.

When
`x=-1`,

`f(x)=(1)/((4+1)(-1+1))=(1)/(0)`

`f(-1)`→∞

So,
`f(x)` has a vertical asymptote at
`-1`.

So,
`4,-1` are the vertical asymptotes of
`f(x)`