Combining Functions by Dividing

This lesson covers how to create a new function by dividing two functions. It explains finding zeros of a function through factoring and graphing, addresses common misunderstandings in simplification, and demonstrates dividing functions f(x) by g(x) and g(x) by f(x). The lesson highlights the importance of handling undefined points and defining the domain of the resulting function. Graphical representations are used to illustrate concepts, emphasizing the need to avoid division by zero.

What are the zeros of a function and how can they be found?

Explain the misunderstanding that can occur when dividing functions.

What happens when you evaluate a simplified expression at a value that makes the original expression undefined?

What is the significance of the x-values that make g of x equal to 0?

How do you determine the domain of the function f divided by g of x?

Describe the process of finding g divided by f of x.

What are the restrictions on x when dividing g of x by f of x?