Lesson 1 Summary

 

In this lesson you saw how radical functions can be used in a variety of applications, including accident-scene investigations. You graphed radical functions and then answered questions using the graph and you determined the equation of a radical function from a given graph.

A radical function is a function where the variable is part of the radicand. The base radical function of has the shape of half of a parabola opening to the right. The domain is {x|x ≥ 0, x ∈ R} and the range is {y|y ≥ 0, y ∈ R}. You can graph radical functions by using transformations of the base function Using the form you can describe the transformations of the base function

Parameter	Value > 0	Value < 0
a	Vertical stretch of graph of by a factor of a.	Vertical stretch of graph of by a factor of a. Graph of reflected in x-axis.
b	Horizontal stretch of graph of by a factor of	Horizontal stretch of graph of by a factor of Graph of reflected in y-axis.
h	Graph of is translated to the right h units.	Graph of is translated to the left h units.
k	Graph of is translated up by k units.	Graph of is translated down by k units.

 

You can also determine the domain and range of any radical function using the ideas of transformations.

 

In Lesson 2 you will study how the graphs of a function and the square root of the same function are related.