Which of these describes this three-piece f at…

Which of these describes this three-piece f at x = 1?

Question 17

MediumOriginal question

$f(x) = x + 1$ for $x < 1$ , $f(1) = 2$ , and $f(x) = 3x - 1$ for $x > 1$ .

Which of these describes this three-piece $f$ at $x = 1$ ?

Continuous and differentiableCorrect answerYour answerContinuous but not differentiableCorrect answerYour answerNeither continuous nor differentiableCorrect answerYour answerDifferentiable but not continuousCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

It is continuous at 1.
The slopes are 1 on the left and 3 on the right: not differentiable.

Worth noting

Matching values make it continuous; differentiable needs matching slopes as well.

Concept: Testing differentiability at a point
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsContinuity at a point

Practise this chapter →

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

Practise this chapter →

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

Which of these describes this three-piece f at x = 1?

Question 17

Explanation