Determine if a function is continuous

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The function defined as $$f(x)=\begin{cases}\dfrac{x^2-4}{x+2}, & x\ne-2 \\[3pt] 4, & x=-2 \\ \end{cases}$$ is not continuous at x=-2. The limit as x approaches -2, calculated as $$\lim_{x\to-2}\frac{x^2-4}{x+2}$$ results in -4, which does not equal the function value of 4 at that point. Therefore, the function fails the continuity test at x=-2.

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$$f(x)=\begin{cases}\dfrac{x^2-4}{x+2}, & x\ne-2 \\[3pt] 4, & x=-2 \\ \end{cases}$$

Determine if its continuous at x=-2
 
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To ensure continuity, we require:

$$\lim_{x\to-2}\frac{x^2-4}{x+2}=4$$

Is this true?
 
MarkFL said:
To ensure continuity, we require:

$$\lim_{x\to-2}\frac{x^2-4}{x+2}=4$$

Is this true?

I just got -4 so no it does not equal 4
 
Hi kendalgenevieve! Welcome to MHB! ;)

kendalgenevieve said:
I just got -4 so no it does not equal 4

Good!
That means it's not continuous.
 

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