Step 1. Set the denominator equal to zero.

Step 2. Solve for x.

Step 3. Plug in that value for x in the numerator. If the numerator does not become zero, then the function does not have a hole. (However, it does have an asymptote.) If the numerator becomes zero, then the function has a hole.

Step 4. Choose two values that are on either side and in the neighborhood of x. Evaluate the given function for these values. Average the outputs.

Step 5. Write your answer as an ordered pair, where the x is the x from Step 2 & y is the average of the two outputs from the evaluation in step 4.

Examples Done by Mr. Vizza

Directions: Please calculate the hole(s) of the following function.

Step 1

x+5=0

Step 2

x=-5

Step 3

x=-5 in the numerator

[2(-5)+10][3(-2)-8]

[-10+10][-6-8]

0(-14)=0

This implies a hole when x=-5.

Step 4

Average the outputs. [-46+-46.06]/2=-46.03

Step 5

The hole occurs at (-5,-46.03)

Problems that You Should Practice

Directions: Please calculate the hole(s) of the following functions.

Additional Supportive Links