A function $f$ is called strictly increasing on an interval $I$ when, for $x_1$ and $x_2$ in $I$ ,

x_1 < x_2

always gives

f(x_1) \le f(x_2)

Correct answerYour answer

x_1 < x_2

always gives

f(x_1) < f(x_2)

Correct answerYour answer

f(x) > 0

at every point of

I

Correct answerYour answer

x_1 < x_2

gives

f(x_1) < f(x_2)

for at least one pairCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Strictly increasing means a larger input always gives a strictly larger output, for every pair of points in $I$ .
With $\le$ in place of $<$ , the function is only increasing: it is allowed to stay level. A positive $f(x)$ says nothing about rising.

Worth noting

The $\le$ version is the definition of increasing, which a constant function also meets.

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

A function fff is called strictly increasing on an interval III when, for x1x_1x1​ and x2x_2x2​ in III,