Q 2. - Precalculus Enhanced with Graphing Utilities

Question

Where is the function $f\left(x\right)=x^2$ increasing? Where is it decreasing? 

Step-by-Step Solution

Answer

The given function increase in interval $\left(0,\infty \right)$ and decrease in interval $\left(-\infty ,0\right)$

Step 1. Definition

If the value of $f\left(x\right)$ is increasing on increasing the value of $x$, then the function is known as an increasing function

If the value of $f\left(x\right)$ is decreasing on increasing the value of $x$, then the function is known as a decreasing function. 

Step 2. Explanation

If we put any value of $x$ between $\left(-\infty ,0\right)$ the value of $y$ decrease and we put any value of $x$ between $\left(0,\infty \right)$ the value of $y$ increase

So, given function increase in interval $\left(0,\infty \right)$  and decrease in interval $\left(-\infty ,0\right)$.