Page 527 - Algebra 1

The parent function for rational functions is y = _1 . x
Math Reasoning
Connect What type of variation is a rational function?
a
By identifying the asymptotes from the form y = _x - b + c and plotting a few
points, the rational function can be graphed.
Vertical Asymptote: x=0
Graphing Using Asymptotes
Identify the asymptotes and graph each function. y=_1 -2
Example
3
Math Reasoning
Generalize State the domain and range of the
1 functiony=_x-4 -2.
x-4 SOLUTION
Step1: Identifytheverticalandhorizontalasymptotes. y = _1 - 2 a = 1, b = 4, and c = -2
x-4
The equation of the vertical asymptote is x = 4.
The equation of the horizontal asymptote is y = -2. Step2: Graphtheasymptotesusingdashedlines. Step 3: Make a table of values.
x
0
2
3
5
6
y
-2_1 4
-2_1 2
-3
-1
-1_1 2
Step4: Plotthepointsandconnectthemwithsmoothcurves.
-
Hint
Choose points that lie on either side of the vertical asymptote so that the curves of the graph will be more accurate.
4
y
Vertical Asymptote
2
O
x
-4
-2
-6
-8
4
2
6
Horizontal
Asymptote
8
512 Saxon Algebra 1
y
8
Horizontal Asymptote: y=0
4
O
x
-8
4
8
-8