Lesson 2: Square Root of a Function

 

Focus

 

In previous mathematics courses you have determined the square root of a number. Is it possible to determine the square root of a function? If so, what do you think the graph of the function would look like?

 

Accelerated motion occurs when the speed of an object changes. In Lesson 1 you looked at the formula d = 5t2 that models an object when it is dropped near Earth. You can use this formula to determine the time an object takes to fall if you know the distance the object falls by rearranging the formula to

 

In this form the formula is a linear function. When graphed, the formula will be a straight line. To algebraically solve this equation for t, you would determine the square root of both sides of the equation. How would the graph of the function's square root be different from the graph of the original function?

In Module 1 you looked at ways to change graphs of functions through transformations and by finding the inverse function. In Lesson 2 you will look at another method to change the graph of a given function by taking the square root of the function.

 

Lesson Outcomes

 

At the end of this lesson you will be able to

• sketch the graph of given the graph of y = f(x), and explain the strategies used
• compare the domain and range of the functions  and y = f(x) and explain why the domain and range might be different

Lesson Question

 

In this lesson you will investigate the following question:

• How does determining the square root of a given function change the graph?

Assessment

 

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 2 Assignment (Download the Lesson 2 Assignment and save it in your course folder now.)
• course folder submissions from Try This and Share activities
• additions to Glossary Terms and Formula Sheet
• work under Project Connection