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