Question

Over what interval is the function in this graph increasing?

Answer 1

A function is increasing if it "points upwards".

Think that you have two inputs $x_1<x_2$ (think of them as being very close to each other). A function $f$ is increasing if

$f(x_1)<f(x_2)$

So, smaller input, smaller output.

So:

• In the first segment on the left, the function is decreasing: if you move with little steps rightwards, the output will get smaller and smaller (the function points to the right bottom)
• In the second segment, the line is constant (it's horizontal). This means that even if you consider a larger input, the output reimains the same
• In the third segment, the function is increasing: if you consider a larger input, the output will be larger as well: the function points to the top right.
• In the fourth segment, the function is decreasing again (look at the first bullet point)

So, the function is increasing in the third segment, which is delimited by

$-2\leq x \leq 3$

Answer 2

This question is based on the increasing function. Therefore,  the correct option is B, $-2\leq x\leq 3$ interval is the function in this graph increasing.

In this question, from the graph we have to observed that over what interval is the function in this graph increasing.

In general, a function is increasing, if graph pointed upwards.

If we have two points $x_1$ and $x_2$ then, we said that function f is increasing if,

$f(x_1) =f(x_2)$.

Therefore, from the given graph it is observed that:

In the first segment on the left, the function is decreasing: if you move with little steps rightwards, the output will get smaller and smaller (the function points to the right bottom).

In the second segment, the line is constant (it's horizontal). This means that even if you consider a larger input, the output remains constant.

In the third segment, the function is increasing. If you consider a larger input, the output will be larger as well: the function points to the top right.

In the fourth segment, the function is decreasing again.

Therefore,  the correct option is B, $-2\leq x\leq 3$ interval is the function in this graph increasing.

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https://brainly.com/question/21753201