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11/19/15 Lesson 4 – 2 Symmetry & Translation Advanced Math/Trig
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Warm – up #25. Square both sides: C(–2, 0) r = 5
But originalSince is negative, then x+2 must be negative! so just graph left half of circle!
Homework LogThurs
11/19
Lesson 4 – 2
Learning Objective: To determine symmetry & graph by translation
Hw: #403 Pg. 228 #1 – 35 odd
11/19/15 Lesson 4 – 2 Symmetry & Translation
Advanced Math/Trig
Learning Objective To determine symmetry To graph by transformation
Symmetric with respect to:
(2, 4)(–2, 4)
y-axis
(4, 2)
(4, –2)
(1, 1)
(–1, –1)
x-axis origin(x, y) (–x, y) (x, y) (x, –y) (x, y) (–x, –y)When plugging in with (–), should get equivalent equation!
Hints for checking for symmetry
Symmetry1. Given the portion of the graph.Complete the graph so it’s symmetric with respect to the y–axis.
(x, y) (–x, y)(0, 3) (0, 3)(1, 0) (–1, 0)(1, 0)
(0, 3)
(1, 0)
(0, 3)
(–1, 0)
Symmetry2. Given the portion of the graph.Complete the graph so it’s symmetric with respect to the x–axis.
(x, y) (x, –y)(0, 3) (0, –3)(1, 0) (1, 0)(1, 0)
(0, 3)
(1, 0)
(0, 3)
(0, –3)
Symmetry3. Given the portion of the graph.Complete the graph so it’s symmetric with respect to the origin.
(x, y) (–x, –y)(0, 3) (0, –3)(1, 0) (–1, 0)(1, 0)
(0, 3)
(1, 0)
(0, 3)
(0, –3)
(–1, 0)
Hints for checking for symmetry
Test for Symmetry & Graph
4. y–axis Plug in –x for x x–axis Plug in –y for y Origin Plug in –x for x and –y for y So it’s symmetric about the y–axis, x–axis, & origin!
Equivalent Eq’n! Yes!
Equivalent Eq’n! Yes!
Equivalent Eq’n! Yes!
Test for Symmetry & Graph
5. y–axis Plug in –x for x x–axis Plug in –y for y Origin Plug in –x for x and –y for y So it’s symmetric about the y–axis
Equivalent Eq’n! Yes!
NO!
NO!
Test for Symmetry & Graph
5. Symmetric about the y–axis
x y –2 –1
161
1 2
116
( 0 0)
Test for Symmetry & Graph
6. y–axis
x–axis
Origin
So it’s symmetric about the x–axis
NO!
Equivalent Eq’n! Yes!
NO!
Test for Symmetry & Graph
7. y–axis x–axisOrigin
So it’s symmetric about the origin
NO!
Equivalent Eq’n! Yes!
NO! (0, 0)
(1, 1)
(–1, –1)
Stretching8.
(Mult each y–coord by 2)
(Mult each y–coord by )
The x–value stays the same in each. It’s only the y–value that changes.
Reflection9. Reflect across the x–axis (x, y) (x, –y)
(1, 1)(–1, –1)
(1, –1)
(–1, 1)
Translation10. Vertical
Up 2
Down 3
Translation11. Horizontal
Right 2
Left 3
Inside of parenthesis,
opposite sign
Transformation12. y = f (x) is shown.Sketch y = 2f (x)Sketch y = f (x) – 2 Sketch y = f (x + 5)Sketch y = – f (x)
Ticket Out the Door Simplify
Homework#403 Pg. 228 #1 – 35 odd
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