Respuesta :

semsee45

Answer:

[tex]\textsf{B.} \quad f(x)=\dfrac{1}{(x+2)(x-1)}[/tex]

Step-by-step 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:

[tex]f(x)=\dfrac{1}{(x+2)(x-1)}[/tex]

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

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