How does f(x) = (x^2 - 4)/(x - 2) if x ≠ 2; 3 if x = 2 behave at x = 2?

Question 18

MediumOriginal question

How does $f(x) = \begin{cases} \frac{x^{2} - 4}{x - 2}, & x \ne 2 \\ 3, & x = 2 \end{cases}$ behave at $x = 2$ ?

Continuous at the pointCorrect answerYour answerNot continuous: the limit exists but differs from the valueCorrect answerYour answerNot continuous: the left and right limits differCorrect answerYour answerNot continuous: the function has no value thereCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Continuity at $a$ needs the left limit, the right limit and $f(a)$ to be equal.
Here the left limit is $4$ , the right limit $4$ and $f(2) = 3$ .

Worth noting

The limit is $x + 2 \to 4$ , but the value given at 2 is 3.

Concept: Testing continuity at a point
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsContinuity at a point

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How does f(x)={x2−4x−2,x≠23,x=2f(x) = \begin{cases} \frac{x^{2} - 4}{x - 2}, & x \ne 2 \\ 3, & x = 2 \end{cases}f(x)={x−2x2−4​,3,​x=2x=2​ behave at x=2x = 2x=2?

Explanation

How does $f(x) = \begin{cases} \frac{x^{2} - 4}{x - 2}, & x \ne 2 \\ 3, & x = 2 \end{cases}$ behave at $x = 2$ ?