# What is the range of a function like f(x)=5x^2?

Jul 23, 2014

The range of $f \left(x\right) = 5 {x}^{2}$ is all real numbers $\ge 0$

The range of a function is the set of all possible outputs of that function.

To find the range of this function, we can either graph it, or we can plug in some numbers for $x$ to see what the lowest $y$ value we get is.

Let's plug in numbers first:

If $x = - 2$: $y = 5 \cdot {\left(- 2\right)}^{2}$, $y = 20$
If $x = - 1$: $y = 5 \cdot {\left(- 1\right)}^{2}$, $y = 5$
If $x = 0$: $y = 5 \cdot {\left(0\right)}^{2}$, $y = 0$
If $x = 1$: $y = 5 \cdot {\left(1\right)}^{2}$, $y = 5$
If $x = 2$: $y = 5 \cdot {\left(2\right)}^{2}$, $y = 20$

The lowest number is 0. Therefore the y value for this function can be any number greater than 0.

We can see this more clearly if we graph the function:

The lowest value of y is 0, therefore the range is all real numbers $\ge 0$