## Calculus 8th Edition

(a) A function $f$ is called even if $f(-x) = f(x)$ for each value $x$ in its domain. An even function can be identified if the graph of the function is symmetric with respect to the y-axis. Three examples of even functions are $f(x) = x^4$, $f(x) = cos(x)$, and $f(x) = \frac{1}{x^2}$. (b) A function $f$ is called odd if $f(-x) = -f(x)$ for each value $x$ in its domain. An odd function can be identified if the graph of the function is symmetric about the origin. Three examples of odd functions are $f(x) = x$, $f(x) = sin(x)$, and $f(x) = x^5$.
(a) $f(x) = x^4$ is an even function because $f(-x) = (-x)^4 = x^4 = f(x)$. $f(x) = cos(x)$ is an even function because $f(-x) = cos(-x) = cos(x) = f(x)$. $f(x) = \frac{1}{x^2}$ is an even function because $f(-x) = \frac{1}{(-x)^2} = \frac{1}{x^2} = f(x)$. (b) $f(x) = x$ is an odd function because $f(-x) = -x = -x = -f(x)$. $f(x) = sin(x)$ is an odd function because $f(-x) = sin(-x) = -sin(x) = -f(x)$. $f(x) = x^5$ is an odd function because $f(-x) = (-x)^5 = -x^5 = -f(x)$.