Page 525 - Algebra 1

L E S S O N Graphing Rational Functions 78
Warm Up
New Concepts
1. Vocabulary A expression is an expression where the
(39)
2. True or False: The graph of the equation x = -2 is a vertical line. (30)
denominator contains a variable and the value of the variable cannot make the denominator equal to zero.
3. True or False: The graph of the equation y = -x is a horizontal line. (30) _
4. Determine when the expression x + 7 is undefined. (43) 3x
A rational function is a function whose rule can be given as a rational expression. This means that a rational function has a variable in the denominator. Rational functions, like rational expressions, are undefined when the denominator is equal to zero.
A value of a variable for which an expression or a function is undefined is 7
called an excluded value. For the function y = _x + 2 , -2 is an excluded value; this is because when x = -2, the function is undefined.
Example
1
Determining Excluded Values
Find_the excluded values. y= m-4
3m - 12 SOLUTION
Simplify the denominator by factoring out the GCF. 3m - 12 = 3(m - 4) The GCF is 3.
Set the denominator equal to zero and solve for m.
Set the denominator equal to zero. Divide both sides by 3.
Simplify.
Add 4 to both sides. Simplify.
Math Reasoning
Verify Show that
m = 4 without factoring out the GCF.
_3 ( m - 4 ) = 0 3(m-4) = 0
Online Connection www.SaxonMathResources.com
m=4
The denominator equals zero when m = 4, so 4 is an excluded value.
_ 33
Reading Math
x ≠ 6 is read, “x is not equal to 6” or “x cannot equal 6”.
m-4= 0 +__4 +__4
m ≠ 4
510 Saxon Algebra 1