September 27 th

September 27th

Write a new equation g(x) compared to f(x) = 4x + 2

1. Shift up 8 2. Shift left 6

Warm-UpFriday, November 1st

Match the Equation to the Translation

G(x) = 2x - 4

1. g(x)=2x -8 2. g(x)= 2(x+5)-43. g(x)=2x + 84. g(x)=2(x-4) - 6

a. Shift up 4 units b. Shift down 4

units c. Shift right 4 and

down 2d. Shift left 5

Horizontal, vertical, or both?!

HOMEWORKANSWERS

What has changed?!

Stretches &

Compressions

Part II-Transformations

1. Stretches and compressions change the slope of a linear function.

2. If the line becomes steeper, the function has been stretched

vertically or compressedhorizontally.

3. If the line becomes flatter, the function has been compressed

vertically or stretched horizontally.

Stretch vs. Compression

1.Stretches=pull away from y axis

2.Compression=pulled toward the y axis

Horizontal vs. Vertical

1.Horizontal=x changes

2.Vertical=y changes

Stretches and Compressions

Stretches and compressions are not congruent to the original

graph. They will have different rates of change!

Use a table to perform a horizontal stretch of the function

y= f(x) by a factor of 3. Graph the function and the transformation on the same coordinate plane.

Step 2: Multiply each x-coordinate by 3.

Think: Horizontal(x changes) Stretch (away from y).

3x x y3(–1) = –3 –1 33(0) = 0 0 03(2) = 6 2 2

3(4) = 12 4 2

#1

Step 1: Make a table of x and y coordinates

Step 3: Graph

Use a table to perform a vertical stretch of y = f(x) by a factor of 2. Graph the transformed function on the

same coordinate plane as the original figure.

Step 2: Multiply each y-coordinate by 2.

Think: vertical(y changes) Stretch (away from y).

#2

Step 1: Make a table of x and y coordinates

Step 3: Graph

x y 2y–1 3 2(3) = 60 0 2(0) = 0 2 2 2(2) = 44 2 2(2) = 4

These don’t change!• y–intercepts in a horizontal stretch or compression• x–intercepts in a vertical stretch or compression

Helpful Hint

Writing New Compressions

and Stretches

.

#1

# 2

.

Let g(x) be a horizontal stretch of

f(x) = 6x -4 by a factor of 2 . Write the rule for g(x), and graph the function. 

# 3