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Point Symmetry and Even-Odd Functions, Slides of Algebra

Applied Science University (ASU)Algebra

Point symmetry in the context of coordinate graphs and algebraic tests for determining symmetry about the origin. It also introduces even and odd functions, their definitions, and graph properties. Examples and exercises are provided for practice.

Typology: Slides

2021/2022

Uploaded on 08/01/2022

fabh_99
fabh_99 🇧🇭

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bg1
PointSymmetry
•
Rotating a figure that has point symmetry
180
o
should look the same.
3.1SymmetryandCoordinateGraphs
PointSymmetry
•
2 points are symmetric with respect to (wrt)
a 3
rd
point “M” if & only if M is the midpoint
of the 2 points.
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pf4
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pf9
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Download Point Symmetry and Even-Odd Functions and more Slides Algebra in PDF only on Docsity!

Point Symmetry

  • Rotating a figure that has point symmetry

o

should look the same.

3.1 Symmetry and Coordinate Graphs

Point Symmetry

  • 2 points are symmetric with respect to (wrt) a 3 rd point “M” if & only if M is the midpoint of the 2 points.
  • The^ graph^ of^ a^ relation^ S^ is^ symmetric^ WRT

the origin if and only if (a,b)  S implies that

(a, b)  S.

Origin Symmetry

Algebraic test for determining point symmetry

about the origin:

Determine whether the graph is symmetric WRT the origin. Example: Your turn...

Remember:

For

every

point

(a,

b),

________

is^ also

on

the

graph.

Give examples of pairs of points that demonstrate x axis symmetry.

Remember:

For

every

point

(a,

b),

________

is^ also

on

the

graph.

Give examples of pairs of points that demonstrate yaxis symmetry.

Determine algebraically whether the functions are even, odd, or neither.

Even functions

  1. Definition: if f(‐x) = ____________ , then f(x) is an even function
  1. Graph: a. The graph of an even function is symmetric about the ____________________. b. If (a, b) is on the graph, so is ____________.
  2. Example of an even function: a. Graph f(x) = x^2 b. The points (2, 4) and ( , ) are on the graph c. f(‐x) =

Even and Odd Functions Summary

Odd functions

  1. Definition: if f(‐x) = ____________ , then f(x) is an odd function
  1. Graph: a. The graph of an odd function is symmetric about the ____________________. b. If (a, b) is on the graph, so is ____________.
  2. Example of an odd function: a. Graph f(x) = 3x b. The points (2, 6) and ( , ) are on the graph c. f(‐x) =

Even and Odd Functions Summary

OddEven Functions Reference Odd Function Graphs Even Function Graphs Odd Function Table Values Even Function Table Values Odd Function Notation Even Function Notation A List of Common Odd/Even Functions Some Common Functions not Odd or Even