1. Restricted Values f(x) g(x) h(x) x x x
Chapter 12
Discovery 1
Restricted Values
1. Complete the table of values for the given rational functions.
f(x)
g(x)
h(x) x x x -3 -2 -1 1 2 3 -3 -2 -1 1 2 3 -3 -2 -1 1 2 3
Determine the restricted values of each function.
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2. Chapter 12
Discovery 1
Restricted Values
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.
function by viewing its graph.
function algebraically.
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3. Simplified Expressions and
Chapter 12
Discovery 2
Simplified Expressions and
Restricted Values
To simplify complete the following steps:
Factor out the GCF, 2x.
Rewrite the GCF as 1.
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4. Simplified Expressions and
Chapter 12
Discovery 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.
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