Question

Write a function that fits the following criteria: ….option D: f(x) = (x - 1) (x - 4) / (x - 3) (x - 5) (x - 6)

Answer 1

Option C

Step-by-step explanation:

In the function below:

`f(x)=((x-4)(x-5))/((x-4)(x-2)(x-6))`

Vertical Asymptote

Canceling the common term reduces the fraction to:

`\begin{gathered} ((x-5))/((x-2)(x-6)) \\ \implies\text{Vertical Asymptote at x=2 and x=6} \end{gathered}`

Hole

The common term is x-4, therefore, there is a hole at x=4.

Zero

If the reduced fraction is set equal to 0.

`((x-5))/((x-2)(x-6))=0\implies x-5=0\implies x=5`

The zero is at x=5.

Horizontal asymptote

Since the degree of the numerator is less than degree of denominator, the horizontal asymptote is at y = 0.

The function that fits the criteria is Option C.