What does it mean when finding the holes of a function?
Answer
In order to find the holes of the function. You'd have to factor both the numerator and the denominator. Once you do that you then have to find any common factors and then set those common factors to equal zero and solve. You do this in order to find the x-coordinates of the holes. Lets break this down into steps.
Step 1. Factor the function.
Before you do anything you have to factor both the numerator and the denominator first.
Step 2. Find any common factors.
Once you factored both numerator and the denominator look for any common factors that you see in the numerator and denominator.
Step 3. Find the x-coordinates.
To find the x-coordinates you have to set each common factor to equal zero and solve for x. From there you will find the values of the x-coordinates of the holes.
Step 4. Find the y-coordinates of the hole.
Lastly, to find the y-coordinates of the hole. You would have to cancel out the common factors of the original expression to get the simplified function. From there you do the same thing to find the holes by setting those factors by zero and solve for y.