Restricted Values

1. Complete the table of values for the given rational functions.

26 2 2. ( ) . ( ) . ( )

1 2

a b cx x x

f x g x h xx x x

x-3-2-10123

-3-2-10123

-3-2-10123

x x

Determine the restricted values of each function.1 of 2

Chapter 9Discovery 1

f(x) h(x)g(x)

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 9Discovery 1

Simplified Expressions andRestricted Values

To simplify complete the following steps:26,

14xx

26 2 314 2 7

2 32 7

31

737

x x xx x

x xx

x

x

Factor out the GCF, 2x.

Rewrite the GCF as 1.

1 of 2

Chapter 9Discovery 2

2 of 2

Simplified Expressions andRestricted Values

Check the equivalence of the expressions and by graphing. Let

and

2614

xx

37x

26Y1

14 x

x3

Y2 .7

x

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 valuesexcept when x = 0.

Chapter 9Discovery 2