consider the function $g(x)=\frac{x^{2}+7x - 18}{x^{2}+2x - 8}$. which type of discontinuity does the…

consider the function $g(x)=\frac{x^{2}+7x - 18}{x^{2}+2x - 8}$. which type of discontinuity does the function have at $x=-4$? jump mixed infinite removable

consider the function $g(x)=\frac{x^{2}+7x - 18}{x^{2}+2x - 8}$. which type of discontinuity does the function have at $x=-4$? jump mixed infinite removable

Answer

Answer:

infinite

Explanation:

Step1: Factor the numerator and denominator

$g(x)=\frac{x^{2}+7x - 18}{x^{2}+2x - 8}=\frac{(x + 9)(x-2)}{(x + 4)(x - 2)}$

Step2: Simplify the function (for $x\neq2$)

$g(x)=\frac{x + 9}{x + 4},x\neq2$

Step3: Analyze the limit as $x\to - 4$

$\lim_{x\to - 4^{-}}\frac{x + 9}{x + 4}=-\infty$ and $\lim_{x\to - 4^{+}}\frac{x + 9}{x + 4}=\infty$. Since the limit approaches infinity as $x$ approaches - 4, the function has an infinite discontinuity at $x=-4$.