Question

Which of the following rational functions is graphed below?

Answer 1

The rational function that is graphed is B

Answer 2

The rational function which is graphed below is:

Option: B

B.
`F(x)=(x)/((x-1)(x+1))`

Explanation:

From the graph of the function we see that the graph has vertical asymptote at x=1 and x= -1

• Also, we know that while finding the vertical asymptote of the rational function we substitute denominator equal to zero and the values of such x will be the vertical asymptote.

• Also, if the line y=0 act as a horizontal asymptote if the degree of polynomial in numerator is smaller than in the denominator.

The function in which above two property hold true is:

B.
`F(x)=(x)/((x-1)(x+1))`

( since in option: A

If denominator equal to 0 then x=0 and -1

This means that the vertical asymptotes are 0 and -1 .

In option: C

If denominator is equal to zero.

Then x=0 and 1

This means that the vertical asymptotes are 0 and 1

In option: D

When denominator=0

then x=0

This means that the vertical asymptote is at x=0

which is false )