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Graphing Functions Basics
Graphing Functions By Including Intercepts
A simple method of graphing only involves plotting points, chosen in more or less
random manner. An improvement to this method involves plotting all intercepts first, and
then plotting some additional points.
Intercepts Method For Graphing Functions
1.
Find and plot all intercepts
. To find yintercepts, let x=0 and solve for y. To find
xintercepts, let y=0 and solve for x.
2.
Plot points on each side of each xintercept
. Find and plot at least one point
between each two xintercepts and one point on each side of the largest and
smallest xintercept.
3.
Draw a smooth curve through the points
from left to right.
Example: Graph f(x) = x
3
– x.
First, rewrite as y = x
3
– x.
Now, find intercepts.
When x = 0, we get y = 0
3
– 0 = 0.
So our yintercept is (0,0)
When y=0, we get 0 = x
3
– x.
We solve this equation. CONTINUED ON NEXT PAGE
0 = x
3
– x
Given
0 = x(x
2
– 1)
Use Distributive Property to factor out x.
0 = x(x + 1)(x – 1)
Use Distributive Property to factor x
2
– 1.
x = 0
The Zero Product Law allows us to let each factor = 0
x + 1 = 0
x – 1 = 0
x =
1
, x =
1
, x =
0
Solve each equation using Addition Property of Equality
So the xintercepts are (
1
,0), (
1
,0), and (
0
,0)
We plot these points to get
Now, find and plot points on each side of each of these xintercepts by letting x= 2,
x=1/2, x=1/2, and x=2. Draw a smooth curve through the points.
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 Fall '09
 Crandall
 Anthropology, Derivative, Graph of a function, single solution, Permission Granted, NonProfit Purposes

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