Question

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

Answer 1

See below

Explanation:

`f(x) = 2sqrtx`

If we are confined to the real numbers, `f(x)` 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(x)` cannot be plotted on the real `xy-`plane for `x<0`.

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

`sqrt([f(x)]^2) = +-2 sqrtx`

This ensures the mapping `f(x) harr x` is one-to-one so that `f(x)` is a true function of `x`.

The graph of `f(x)` is shown below.

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