Module 2: Radical Functions

 

Lesson 2 Summary

 

In this lesson you looked at the graph of when given the graph of y = f(x). You can use the values from the function f(x) to predict the values of the function The y-values of the points of  are the square roots of the y-values of the points on the original function y = f(x).

 

In terms of mapping: so The invariant points occur when f(x) = 0 and f(x) = 1 because the square root of 0 is 0 and the square root of 1 is 1. The domain of  are the x-values of f(x) for which f(x) is greater than or equal to zero. The range of  are the y-values in the range of f(x) for which f(x) is defined.

 

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 graph is above y = f(x) graph graph intersects y = f(x) graph graph is below y = f(x) graph

 

Some of the key lesson points are highlighted on the following 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.

 

In Lesson 3 you will study how the graphs of radical functions can help solve radical equations.