Increasing & Decreasing Functions (College Board AP® Precalculus): Study Guide

Discriminating between open and closed intervals for where a function is increasing or decreasing is outside the scope of the AP® Precalculus course and exam.

This means that in your AP® Precalculus course you will not have to worry about the endpoints on intervals where a function is increasing or decreasing.

• E.g. the point in between an interval where a function is increasing and an interval where it is decreasing

Behavior at such endpoints is studied in AP® Calculus.

The figure shows the graph of $f$ on its domain $a\le x\le e$. The $x$ coordinates of local maximum and minimum points are indicated. On which interval(s) in its domain is $f$ increasing?

(A) $\left(b,c\right)\mathrm{only}$

(B) $\left(c,d\right)\mathrm{only}$

(C) $\left(a,b\right)\mathrm{and}\left(c,d\right)$

(D) $\left(b,c\right)\mathrm{and}\left(d,e\right)$

Answer:

Look for regions where the value of $y$ is increasing (i.e. the graph goes up) as the value of $x$ increases (i.e. the graph goes to the right)

• This happens between $b$ and $c$, AND between $d$ and $e$

(D) $\left(b,c\right)\mathrm{and}\left(d,e\right)$