Which of the following functions has a hole at (1,4)? answer choices in the image below! provide work with your )! you!

The answer is:

d)

A hole is a point where rational functions lose its continuity, meaning that in that point, there is a discontinuity condition.

We can find the hole of a rational function if there are similar terms on the numerator and the denominator by finding:

First (x-component): The values of x that makes the function equal to 0 in both numerator and denominator.

Second (y-component): Re-evaluating the same term in the other factors of the function to know the y-component.

Finding the x component we have:

So, the x-component is 1,

Then, re-evaluating the function:

Therefore, the y-component is 4,

Hence,

The function has a hole at (1,4)

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