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Find all discontinuities of the function g(x) = \frac{2x^2 - 14x + 24}{3x^2 - 6x - 9} . Use...

Question:

Find all discontinuities of the function {eq}g(x) = \frac{2x^2 - 14x + 24}{3x^2 - 6x - 9} {/eq}. Use limits to determine what type each discontinuity is.

Continuity of Rational Functions:

Rational functions are functions of the form {eq}f\left ( x \right )=\frac{P\left ( x \right )}{Q\left ( x \right )} {/eq} where {eq}P(x) {/eq} and {eq}Q(x) {/eq} are polynomials. Rational functions are continuous for all real numbers except for those values of {eq}x {/eq} for which the denominator is equal to zero.

Answer and Explanation:

{eq}\begin{align*} \lim_{x\rightarrow 3}\frac{2\left ( x-4 \right )\left ( x-3 \right )}{3\left ( x-3 \right )\left (x+1 \right...

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Rational Function: Definition, Equation & Examples

from GMAT Prep: Help and Review

Chapter 10 / Lesson 11
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