Thursday, November 14th Warm-Up Write a new equation g(x) compared to f(x) = 1/2x + 2 Shift up 7 Shift left 4 September 27th
What has changed?! F(x) G(x)
Part II-Transformations Stretches & Compressions
Stretches and compressions change the slope of a linear function. If the line becomes steeper, the function has been stretched vertically or compressed horizontally. 3. If the line becomes flatter, the function has been compressed vertically or stretched horizontally.
Stretch vs. Compression • Stretches=pull away from y axis • Compression=pulled toward the y axis
Horizontal vs. Vertical • Horizontal=x changes • Vertical=y changes
Stretches and compressions are not congruent to the original graph. They will have different rates of change! Stretches and Compressions
#1 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. Think: Horizontal(x changes) Stretch (away from y). Step 1: Make a table of x and y coordinates Step 2: Multiply each x-coordinate by 3. Step 3: Graph
#2 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. Think: vertical(y changes) Stretch (away from y). Step 1: Make a table of x and y coordinates Step 2: Multiply each y-coordinate by 2. Step 3: Graph
Helpful Hint • These don’t change! • y–intercepts in a horizontal stretch or compression • x–intercepts in a vertical stretch or compression
Writing New Compressions and Stretches
# 3 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. .