How does f(x) = 3 - x if x < 2; x - 1 if x ≥ 2 behave at x = 2?

Continuity & Differentiability · Question 3 of 125

Question 3

EasyOriginal question

How does $f(x) = \begin{cases} 3 - x, & x < 2 \\ x - 1, & x \ge 2 \end{cases}$ behave at $x = 2$ ?

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

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Continuity at $a$ needs the left limit, the right limit and $f(a)$ to be equal.
Here the left limit is $1$ , the right limit $1$ and $f(2) = 1$ .

Worth noting

$3 - 2 = 1$ and $2 - 1 = 1$ : the two pieces meet at $x = 2$ .

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)={3−x,x<2x−1,x≥2f(x) = \begin{cases} 3 - x, & x < 2 \\ x - 1, & x \ge 2 \end{cases}f(x)={3−x,x−1,​x<2x≥2​ behave at x=2x = 2x=2?

Explanation

How does $f(x) = \begin{cases} 3 - x, & x < 2 \\ x - 1, & x \ge 2 \end{cases}$ behave at $x = 2$ ?