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ref_1.pptCopyright © 2013 Pearson Education, Inc. All rights reserved
Section 2.1
Intercepts; Symmetry; Graphing Key Equations
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Find the x-intercept(s) and the y-intercept(s) of the graph of then graph by plotting points.
To find the x-intercept(s), let y = 0.
To find the y-intercept(s), let x = 0.
Copyright © 2013 Pearson Education, Inc. All rights reserved
Now find and plot some points.
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
If a graph is symmetric with respect to the x-axis and the point (3,2) is on the graph, what other point is also on the graph?
(3,2)
(3,–2)
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
If a graph is symmetric with respect to the y-axis and the point (3,2) is on the graph, what other point is also on the graph?
(–3, 2)
(3,2)
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
If a graph is symmetric with respect to the origin and the point (3,2) is on the graph, what other point is also on the graph?
(–3, –2)
(3,2)
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
x-Axis:
Not equivalent so not symmetric with respect to the x-axis.
y-Axis:
IS equivalent so symmetric with respect to the y-axis.
Origin:
Not equivalent so not symmetric with respect to the origin.
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
2
4
yx
=-
x
2
-
4
=
0
x
+
2
(
)
x
-
2
(
)
=
0
x
+
2
=
0
o
r
x
-
2
=
0
x
=
-
2
o
r
x
=
2
y
=
x
2
-
4
y
=
0
2
-
4
=
-
4
2
2
9
Test for symmetry.
2
x
y
x
-
=
+
2
2
9
2
x
y
x
-
-=
+
(
)
(
)
2
2
9
2
x
y
x
--
=
-+
(
)
(
)
2
2
9
2
x
y
x
--
-=
-+
-4
-3
-2
-1
1
2
3
4
5
-4
-3
-2
-1
1
2
3
4
