Chapter 2.4, Problem 4AYU

The function $f\left(x\right)=x^2$ is decreasing on the interval ______.

To determine

To fill: The decreasing interval of the function $f\left(x\right)=x^2$.

Answer to Problem 4AYU

Solution:

The function $f\left(x\right)=x^2$ is decreasing on the interval $\left(-\infty ,0\right]$.

Explanation of Solution

Given:

It is asked to find the decreasing interval of the function $f\left(x\right)=x^2$.

The domain of the square function is the set of all real numbers; its range is the set of non-negative real numbers. The graph of this function is a parabola whose intercept is at $\left(0,0\right)$. The square function is an even function that is decreasing on the interval $\left(-\infty ,0\right]$ and increasing on the interval $\left[0,\infty \right)$.