Question

Which of the following rational functions is graphed below?

option D. F(x) = (x-1)/ x(x+2)

Answer 1

The rational function graphed is C

Explanation:

We simply analyze the graph given to deduce its properties and consequently identifying the rational function with the matched characteristics.

From the graph, it is evident that the rational function has two vertical asymptotes;

one along the y-axis; the line x = 0

the other at x = 3

The vertical asymptotes represents undefined points or points of discontinuity of the function. That is to imply the the function is not defined at these points.

For a rational function, the function will be defined everywhere except where the expression in the denominator becomes zero. In our case, the expression in the denominator becomes zero when;

x = 0 and x = 3

Therefore, the expression in the denominator will be of the form;

x(x-3)

so that when equated to 0 we have

x(x-3)=0

x=0 or x-3=0

x=0 or x =3

The rational function graphed is thus C

Answer 2

C

Explanation:

From the diagram you can see that the graph of the function has two vertical asymptotes: x=0 and x=3.

A. This function is undefined when the denominator

`(x+3)(x-2)=0\\ \\x=-3 \text{ or } x=2`

Thus, vertical asymptotes are x=-3 and x=2.

B. This function is undefined when the denominator

`(x+2)^2=0\\ \\x=-2`

Thus, vertical asymptote is x=-2.

C. This function is undefined when the denominator

`(x)(x-3)=0\\ \\x=0 \text{ or } x=3`

Thus, vertical asymptotes are x=0 and x=3.