Which of following rational functions is graphed below A. f(x) (1)/(6x) B. f(x) (1)/(x + 6) C. f(x) (1)/(x - 6) D. f(x) (x)/(6)

Question

Which of following rational functions is graphed below

A.

`f(x) (1)/(6x)`


B.

`f(x) (1)/(x + 6)`


C.

`f(x) (1)/(x - 6)`

D.

`f(x) (x)/(6)`

Answer 1

The correct option is C.

Explanation:

The parent rational function is

`g(x)=(1)/(x)`

The vertical asymptote of this function is y-axis.

From the given graph it is clear that the vertical asymtote of the given function is x=6. It means the function is not defined for x=6.

The function is not defined at x=6 if the denominator of the function is 0 at x=6.

The function
`f(x)=(1)/(x-6)` is not defined for x=6.

Therefore the correct option is C.