Chapter 4.1, Problem 9AYU

The graphs of power functions of the form $f(x)=x^n$, where $n$ is an even integer, always contain the points ________, _______, and ______.

To determine

To find: The graph of power functions of the form $f\left(x\right)=x^n$ where $n$ is an even integer; always contain the point’s _____, ______ and _____.

Answer to Problem 9AYU

The graph of power functions of the form $f\left(x\right)=x^n$ where $n$ is an even integer; always contain the point’s $\left(-1,1\right)$, $\left(0,0\right)$ and $\left(1,1\right)$.

Explanation of Solution

Given:

$f\left(x\right)=x^n$

The graph is symmetric with respect to $y\text{-axis}$. The domain is set of all real numbers. The range is the set of non-negative numbers.

The graph of power functions of the form $f\left(x\right)=x^n$ where $n$ is an even integer; always contain the point’s $\left(-1,1\right)$, $\left(0,0\right)$ and $\left(1,1\right)$.