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: |
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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: |
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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: |
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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: |