Chapter 1 Functions & Graphs Mr. J. Focht PreCalculus OHHS

1.6 Graphical Transformations Transformations Vertical & Horizontal Translations Reflections Across Axes Vertical & Horizontal Stretches & Shrinks Combining Transformations

Vocabulary Transformations change graphs. Rigid Transformations leaves the size and shape of the graph unchanged. Non-Rigid Transformations distort the shape of the graph.

Class Work Do Exploration 1 on p. 138 To type Y 1 (X)+3 into the calculator, follow these steps.

What You Explored

Class Work P. 147, #3

Example The red dashed curve is f(x) = x 3. Find the function for the blue curve. g(x) = x 3 + 3h(x) = x 3 -3 j(x) = (x-3) 3 k(x) = (x+3) 3

Example The red dashed curve is f(x) = x 3. Find the function for the blue curve. g(x) = x 3 + 3h(x) = x 3 -3 j(x) = (x-3) 3 k(x) = (x+3) 3

Class Work P. 148, #25

Example Reflect A over the x-axis. Reflect A over the y-axis. Reflect A over the line y = x. E D H

Reflections

Example Find an equation for the reflection of over each axis. x-axis: y = -f(x) = y-axis: y = f(-x) =

Verify by Graphing To avoid confusion, I just turned 2 graphs on at a time.

Class Work P. 148, #29

Class Work P. 143, Exploration 2

Class Work P. 144, Exploration 3

Class Work

Stretches & Shrinks A vertical stretch is when the graph is pulled up – elongating the graph. A vertical shrink is when the graph is pushed down – flattening the graph.

Example of a Vertical Stretch y=|x|y=2|x|

Example of a Vertical Shrink y=0.5|x| y=|x|

A horizontal stretch pulls from both sides of the graph. A horizontal shrink pushes in on both sides of the graph.

Example of a Horizontal Stretch y=|x|

Example of a Horizontal Shrink y=|x|

Example y 1 = f(x) = x 3 – 16x a) Find y 2 that is a vertical stretch of y 1 by a factor of 3. y 2 = 3 f(x) = 3(x 3 – 16x) = 3x 3 – 48x b) Find y 3 that is a horizontal shrink of y 1 by a factor of ½ =(2x) 3 -16(2x) = 8x 3 – 32x

Class Work P. 148, #39

Home Work P #4, 6, 8, 10, 12, 14, 16, 17, 18, 26, 32, 41, 52, 59-64