How does f(x) = (x^2 - 9)/(x - 3) behave at x = 3?

Question 10

EasyOriginal question

How does $f(x) = \frac{x^{2} - 9}{x - 3}$ behave at $x = 3$ ?

Not continuous: the function has no value thereCorrect answerYour answerContinuous at the pointCorrect answerYour answerNot continuous: the limit exists but differs from the valueCorrect answerYour answerNot continuous: the left and right limits differCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

At $x = 3$ the formula gives $\frac{0}{0}$ : 3 is not in the domain, so $f(3)$ does not exist.
The limit $x + 3 \to 6$ exists, but with no value at 3 there is nothing for it to equal.

Worth noting

A limit is not a value: $\frac{x^{2} - 9}{x - 3}$ tends to 6 at 3 but is not defined there.

Concept: Testing continuity at a point
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsContinuity at a point

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Ten questions from Continuity & Differentiability, at your own pace.

How does f(x)=x2−9x−3f(x) = \frac{x^{2} - 9}{x - 3}f(x)=x−3x2−9​ behave at x=3x = 3x=3?

Explanation

How does $f(x) = \frac{x^{2} - 9}{x - 3}$ behave at $x = 3$ ?