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12345More power functions

## Theory

Take a look at the applet: Power Functions

A power function is a function of the form $f\left(x\right)=a{\left(x+b\right)}^{p}+c$, where $p$ can also take any real value. This sort of function is derived by transformation from $y={x}^{p}$. A few examples:

• $p=0$:
$f\left(x\right)=a+c$ a constant function.

• $p=1$:
$f\left(x\right)=ax+d$ a linear function.

• $p=2$:
$f\left(x\right)=a{\left(x+b\right)}^{2}+c$ a quadratic function.

• $p=\frac{1}{2}$:
$f\left(x\right)=a{\left(x+b\right)}^{\frac{1}{2}}+c=a\sqrt{x+b}+c$ a radical function.

• $p=-1$:
$f\left(x\right)=a{\left(x+b\right)}^{-1}+c=\frac{a}{x+b}+c$ a hyperbolic function.