Question

The graph shown here is the graph of which of the following rational

functions?
FO
6

Answer 1

Look at the vertical asymptotes

They are

• x=-2
• x=1

So factor up the denominator

• (x+2)(x-1)≠0

Hence the rational function is 1/(x+2)(x-1)

Option B

Answer 2

`\textsf{B.} \quad f(x)=(1)/((x+2)(x-1))`

Explanation:

Asymptote: a line which the curve gets infinitely close to, but never touches.

From inspection of the graph, we can see that the asymptotes are:

• x = -2
• x = 1
• y = 0

This means that the function is undefined when x = -2, x = 1 and y = 0.

For a rational function to be undefined, the denominator equals zero.

Therefore,

• x = -2 ⇒ (x + 2) = 0
• x = 1 ⇒ (x - 1) = 0

So the equation of the function is:

`f(x)=(1)/((x+2)(x-1))`