Today in Pre-Calculus

• Do NOT need a calculator• Go over homework• Notes: Non-Rigid Graphical

Transformations• Homework

Homework2) up 5.24) Right 36) Down 1008)Left 50 down 27910)Right 518)Reflect over x-axis, left 430)

Non-Rigid Transformations• Changes the size and shape of the graph.

• Types:

– Stretches

– Shrinks

– Can be vertical or horizontal

Vertical• Multiply equation by a factor c: y = c∙f(x)

• If c > 1, stretch by a factor of c

• If c < 1, shrink by a factor of c

y=x3-5x

y=2(x3-5x)

y=1/2(x3-5x)

Horizontal• Divide the x in the function by c:• If c > 1, stretch by a factor of c• If c < 1, shrink by a factor of c

y=x3-5x

y=(x/3)3-5(x/3)

y=(x/.5)3-5(x/.5)

xy f

c

Misc• Reflections: If c is negative in either the vertical

or horizontal stretch/shrink, the graph reflects and stretches/shrinks.

• Order matters when combining transformations1) Stretch/shrink

2) Reflections

3) Shifts

Example

Basic function: x2

Key points: (0,0), (1,1), (-1,1)

Vertical stretch 3 (multiply y by 3)

Down 4

2( ) 3 4f x x

Example

Basic function: x3

Key points: (0,0), (1,1), (-1,-1)

Reflect over x-axis

Vertical stretch 1/2 (multiply y by 1/2)

Right 3

31( ) 3

2f x x

Example

y = f(x – 2) + 3

b. y = 0.5f(x + 1) – 2 c.

0.5 1 2y f x

2 1 3y f x

Homework• Pg 147: 13-16, 21, 24, 26, 39, 43, 44, 47, 49, 51-

54(use handout)

• Memorize 10 basic functions

• Quiz Monday, September 29