Power function

Power functions

Real functions of the form ${\displaystyle f(x)=cx^{n}}$, where ${\displaystyle c\neq 0}$, are sometimes called power functions. When ${\displaystyle n}$ is an integer and ${\displaystyle n\geq 1}$, two primary families exist: for ${\displaystyle n}$ even, and for ${\displaystyle n}$ odd. In general for ${\displaystyle c>0}$, when ${\displaystyle n}$ is even ${\displaystyle f(x)=cx^{n}}$ will tend towards positive infinity with increasing ${\displaystyle x}$, and also towards positive infinity with decreasing ${\displaystyle x}$. All graphs from the family of even power functions have the general shape of ${\displaystyle y=cx^{2}}$, flattening more in the middle as ${\displaystyle n}$ increases. Functions with this kind of symmetry(${\displaystyle f(-x)=f(x)}$) are called even functions.