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

Question

Charles Arocha · Accepted Answer

See below

#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]}

Axel Alvarez · Answer

undefined To graph $ f(x) = 2\sqrt{x} $, follow these steps:

1. Choose values for $ x $ (input values) and calculate the corresponding $ f(x) $ (output values).
2. Plot the points obtained from step 1 on the coordinate plane.
3. Connect the points with a smooth curve to form the graph of the function.

For example, when $ x = 0 $, $ f(0) = 2\sqrt{0} = 0 $. Plot the point (0, 0).

Similarly, when $ x = 1 $, $ f(1) = 2\sqrt{1} = 2 $. Plot the point (1, 2).

Continue this process for other values of $ x $ to get more points and then connect them to form the graph.