1. Restricted Values 1. Complete the table of values for the given rational functions. x -3 -2 0 1 2 3 -3 -2 0 1 2 3 -3 -2 0 1 2 3 xx Determine the restricted values of each function. 1 of 2 Chapter 9 Discovery 1 f(x)h(x)g(x)

2. Restricted Values 2 of 2 2. Graph the given rational functions on a calculator screen, (-9.4, 9.4, 1, -6.2, 6.2, 1, 1). Trace each function’s graph. What happens when you reach the point on a graph for the restricted x-values found in exercise 1? Write a rule for determining the restricted values of a rational function by viewing its table of values. Write a rule for determining the restricted values of a rational function by viewing its graph. Write a rule for determining the restricted values of a rational function algebraically. Chapter 9 Discovery 1

3. Simplified Expressions and Restricted Values To simplify complete the following steps: Factor out the GCF, 2x. Rewrite the GCF as 1. 1 of 2 Chapter 9 Discovery 2

4. 2 of 2 Simplified Expressions and Restricted Values Check the equivalence of the expressions and by graphing. Let and 1. Both graphs appear to be coinciding. However, look at the table of values for x = -3, -2, -1, 0, 1, 2, and 3. What do you see? 2. Determine the restricted values for each expression. 3. Explain why the two expressions are equivalent for all values except when x = 0. Chapter 9 Discovery 2