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)

Have a nice day!

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

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