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

1 Answer
Nov 10, 2017

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]}