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At what points is the function y = \frac{x + 9}{x^2 - 14x + 45} continuous? Describe the set of...

Question:

At what points is the function {eq}y = \frac{x + 9}{x^2 - 14x + 45} {/eq} continuous? Describe the set of {eq}x {/eq}-values where the function is continuous, using interval notation.

Continuity of Rational Functions:

Rational functions are continuous for all real numbers in the domain of the rational function. Therefore, rational functions are continuous for all x-values except where the denominator is equal to zero.

Answer and Explanation:

To find the set of x-values for which {eq}y = \frac{x + 9}{x^2 - 14x + 45} {/eq} is continuous, we must find the zeros of the denominator.

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Rational Function: Definition, Equation & Examples

from GMAT Prep: Help and Review

Chapter 10 / Lesson 11
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