Module 2: Radical Functions

 

During Try This 1 and Try This 2, you began to notice patterns between the graphs of y = f(x) and Do these patterns help you graph the square root of any function?

 

Your chart from Try This 2, which summarizes the patterns between the graphs of y = f(x) and , may or may not look similar to the following chart. However, the patterns should be similar. This chart arranges the patterns by the value of the original function, y = f(x), and the effect on the graph of the square root of the function,

 

f(x) f(x) < 0 f(x) = 0 0 < f(x) < 1 f(x) = 1 f(x) > 1

graph

Note: Take the square root of the y-values of y = f(x), and the range must be positive.

 graph undefined and y = f(x) graphs intersect on x-axis. This is an invariant point. graph is above y = f(x) graph graph intersects y = f(x) graph. This is an invariant point. graph is below y = f(x) graph

This illustration shows the graphs of two functions. One is a graph of a linear function labeled f at x. The other graph is the function y equals the square root of f at x; it is a half parabola opening to the right. The invariant points are labelled at (-1, 0) and (-0.5, 1). The graph of y equals the square root of f at x and is above the line y equals f at x when the y values are from zero to one. The square root function is below the line y equals f at x when the y values are greater than one.

 

Based on the patterns you have seen throughout Lesson 2, you will see how to graph when given the graph y = f(x). Go to Graphing the Square Root of a Function.

 

 

This play button opens Graphing the Square Root of a Function.

 

Self-Check 1


textbook

Complete question 4 on page 87 of the textbook. Answer