Over what interval is the function in this graph increasing ?

Accepted Solution

A function is increasing if it "points upwards".Think that you have two inputs [tex] x_1<x_2 [/tex] (think of them as being very close to each other). A function [tex] f [/tex] is increasing if[tex] f(x_1)<f(x_2) [/tex]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 sameIn 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[tex] -2\leq x \leq 3 [/tex]