Read the two statements and choose the correct option. I. f(x) = ax + b is strictly increasing on R when a > 0. II. f(x) = ax + b is strictly decreasing on R when b < 0.

Increasing & Decreasing Functions · Question 3 of 74

Question 3

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Read the two statements and choose the correct option.
I. $f(x) = ax + b$ is strictly increasing on $\mathbb{R}$ when $a > 0$ .
II. $f(x) = ax + b$ is strictly decreasing on $\mathbb{R}$ when $b < 0$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$f(x_2) - f(x_1) = a(x_2 - x_1)$ , so the sign of $a$ alone decides: I is true.
$b$ only moves the line up or down; it changes nothing about rising or falling, so II is false.

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

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