Question

Square Root of a Function: Sketch the graph of the function y = √f(x) given the graph of the function y = f(x). Please provide a detailed sketch or description of the graph of y = √f(x) based on the graph of y = f(x).

Answer 1

To sketch the graph of y = √f(x) given the graph of y = f(x), the square root function (√x) takes the positive square root of the input value. So, for each point (x, y) on the graph of y = f(x), the corresponding point on the graph of y = √f(x) will have the same x-coordinate and the square root of the y-coordinate.

Step-by-step explanation:

To sketch the graph of y = √f(x) given the graph of y = f(x), we need to understand how the square root function affects the graph of the original function. The square root function (√x) takes the positive square root of the input value. So, for each point (x, y) on the graph of y = f(x), the corresponding point on the graph of y = √f(x) will have the same x-coordinate and the square root of the y-coordinate. This means that the graph of y = √f(x) will have the same shape as the graph of y = f(x), but the y-values will be the square roots of the original y-values.