Power Function

1.What is а power function?

• A power function is a single-term function that contains a variable at its base and a constant for its exponent.

• A power function is a function whose (output) value is the same for every input value.

• A power function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc

General form of power function:

• f(x)=lg(x)

• f(x)=a^x

• f(x)=kx^n

Is the function even or odd?

 $f\left(x\right)=\frac{\left(x+2\right)^3}{2}$  

• even

• neither

• odd

Find the domain of the function:

•  $\left(1;\ +\infty\right)$  

•  $\left(-4;\ +\infty\right)$  

•  $\left(-\infty;+\infty\right)$  

 $f\left(x\right)=-5x^2+1$  

Find the range of this power function:

•  $\left(-\infty;+\infty\right)$  

•  $\left(-\infty;1\right]$  

•  $\left(-\infty;1\right)$  

What is the equation of the function graphed in the image?

• $f\left(x\right)=x^{\frac{1}{4}}$

• $f\left(x\right)=\frac{x^3}{4}$

• $f\left(x\right)=\sqrt{x}$

Which one is a power function?

• $f\left(x\right)=4^x+46$

• $f\left(x\right)=\frac{1}{x}-8$

• $f\left(x\right)=7x^2$