How does f(x) = | x - 2 | behave at x = 2?

Continuity & Differentiability · Question 5 of 125

Question 5

EasyOriginal question

How does $f(x) = \lvert x - 2 \rvert$ behave at $x = 2$ ?

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

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Continuity at $a$ needs the left limit, the right limit and $f(a)$ to be equal.
Here the left limit is $0$ , the right limit $0$ and $f(2) = 0$ .

Worth noting

A corner is not a break: both sides tend to 0, which is $f(2)$ .

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

The rule this testsContinuity at a point

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How does f(x)=∣x−2∣f(x) = \lvert x - 2 \rvertf(x)=∣x−2∣ behave at x=2x = 2x=2?

Explanation

How does $f(x) = \lvert x - 2 \rvert$ behave at $x = 2$ ?