# How do you graph f(x) = 2sqrtx?

Nov 10, 2017

See below

#### Explanation:

$f \left(x\right) = 2 \sqrt{x}$

If we are confined to the real numbers, $f \left(x\right)$ is only defined for positive values of $x$ and the value $0$.

This is because the square root of a negative number is complex.

Hence, $f \left(x\right)$ cannot be plotted on the real $x y -$plane for $x < 0$.

Also interesting in this area. When we plot $f \left(x\right)$ we use the so called 'Principal Square Root' which is only the positive values of $f \left(x\right)$ although:

$\sqrt{{\left[f \left(x\right)\right]}^{2}} = \pm 2 \sqrt{x}$

This ensures the mapping $f \left(x\right) \leftrightarrow x$ is one-to-one so that $f \left(x\right)$ is a true function of $x$.

The graph of $f \left(x\right)$ is shown below.

graph{2sqrtx [-14.12, 14.36, -6.76, 7.48]}