Transcript Section P.1 * Graphs and Models

Section P.1 – Graphs and
Models
How to Graph
Make a table to graph y = x2 + 2
Only use a ruler if the relation is linear.
You do not need to plot every point, but make sure
to get the complete graph.
x
y
-5
-4
-3
-2
27
18
11
6
-1
0
1
2
3
4
3
2
3
6
11
18
5
27
Use your
knowledge of
relations and
functions to
make sure
you pick
values of x
that make a
complete
graph.
Definitions
x-intercept Where the graph crosses the x-axis
OR The value of x when y is 0.
y-intercept Where the graph crosses the y-axis
OR The value of y when x is 0.
Types of Symmetry
With Respect to the…
y-axis
x-axis
origin
Replacing y in the
equation by –y yields
an equivalent
equation.
Replacing x in the
equation by –x and y
by –y yields an
equivalent equation.
Tests…
Replacing x in the
equation by –x yields
an equivalent
equation.
Example of Symmetry
Test for symmetry in the equation yx4.
Check out the graph first.
Test by Replacing x in the
equation by –x.
y
 x
4
yx
4An equivalent
equation.
The equation is symmetric with
respect to the y-axis.
System of Equations Example
Solve the following system of equation algebraically:
Both equations
equal y. Set them
equal to each
other.
y  2x  22
y  3x  28
2x  22  3x  28
22  5x  28
50  5x
10  x
y  3 10  28
y  30  28
y2
10, 2
System of Equations Example
Solve the following system of equation algebraically:
2 x  2 y  18
x  3 y
2  3  y   2 y  18
6  2 y  2 y  18
6  18
FALSE
No Solution.
The two lines are
parallel. They
never intersect.
System of Equations Example
Solve the following system of equation algebraically:

2
x
y
2
x
2
22
2
y 3x28
y
y

3
1
02

8



2
x

2
2

3
x

2
8

3
02
8
2
2

5
x

2
8y
y
2
5
05
x
10,2
1
0x