On which interval is f(x) = | x - 2 | strictly decreasing?

Increasing & Decreasing Functions · Question 10 of 74

Question 10

MediumOriginal question

On which interval is $f(x) = \lvert x - 2 \rvert$ strictly decreasing?

(2, \infty)

Correct answerYour answer

(-2, \infty)

Correct answerYour answer

(-\infty, 2)

Correct answerYour answer

\mathbb{R}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

For $x < 2$ , $f(x) = 2 - x$ : as $x$ grows, $f$ falls.
For $x > 2$ , $f(x) = x - 2$ , which rises. So $f$ is strictly decreasing on $(-\infty, 2)$ .

Worth noting

$(2, \infty)$ is where the graph's right arm rises.

Ten questions from Increasing & Decreasing Functions, at your own pace.

Ten questions from Increasing & Decreasing Functions, at your own pace.