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# For what real numbers is the function not continuous? For which of those is the discontinuity removable?

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Consider the function below. List the answers.

$$\displaystyle{f(x)=\frac{{x^{2}-x-6}}{{x^{2}-3x-10}}}$$

For what real numbers is the function not continuous?

For which of those is the discontinuity removable?

Feb 23, 2022

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Factor as   ( x -3) (x + 2)

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( x - 5) ( x + 2)

The function is not continuous at x values that make the denominator = 0   ⇒ x= 5  and x = -2

We have a removable discontinuity  at    x + 2 = 0  ⇒     x =  -2

Feb 23, 2022