Here are the steps required for Finding the Domain of a Rational Function:

 Step 1: A rational function is simply a fraction and in a fraction the denominator cannot equal zero because it would be undefined. To find which numbers make the fraction undefined, create an equation where the denominator is not equal to zero. Step 2: Solve the equation found in step 1. Step 3: Write your answer using interval notation.

Example 1

 Step 1: A rational function is simply a fraction and in a fraction the denominator cannot equal zero because it would be undefined. To find which numbers make the fraction undefined, create an equation where the denominator is not equal to zero. Step 2: Solve the equation found in step 1. In this case, subtract 4 from each side. Step 3: Write your answer using interval notation. In this case, since x ≠ –4 we get:

Example 2

 Step 1: A rational function is simply a fraction and in a fraction the denominator cannot equal zero because it would be undefined. To find which numbers make the fraction undefined, create an equation where the denominator is not equal to zero. Step 2: Solve the equation found in step 1. In this case, we need to factor the problem. Step 3: Write your answer using interval notation. In this case, since x ≠ –2 and x ≠ 7 we get:

Example 3

 Step 1: A rational function is simply a fraction and in a fraction the denominator cannot equal zero because it would be undefined. To find which numbers make the fraction undefined, create an equation where the denominator is not equal to zero. Step 2: Solve the equation found in step 1. In this case, we need to factor the problem. Step 3: Write your answer using interval notation. In this case, since and we get:

Example 4

 Step 1: A rational function is simply a fraction and in a fraction the denominator cannot equal zero because it would be undefined. To find which numbers make the fraction undefined, create an equation where the denominator is not equal to zero. Step 2: Solve the equation found in step 1. In this case, we need to factor the problem. Step 3: Write your answer using interval notation. In this case, since and we get:

Example 5

 Step 1: A rational function is simply a fraction and in a fraction the denominator cannot equal zero because it would be undefined. To find which numbers make the fraction undefined, create an equation where the denominator is not equal to zero. Step 2: Solve the equation found in step 1. In this case, we need to factor the problem. Step 3: Write your answer using interval notation. In this case, since x ≠ –4, x ≠ 0, and x ≠ 2 we get: