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September 27 th

Friday, November 1 st. Warm-Up. Write a new equation g(x) compared to f(x) = 4x + 2 Shift up 8 Shift left 6. September 27 th. Match the Equation to the Translation. G(x) = 2x - 4 g(x )=2x -8 g (x )= 2(x+5)-4 g (x)=2x + 8 g(x )=2(x-4) - 6. Shift up 4 units

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September 27 th

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  1. Friday, November 1st Warm-Up Write a new equation g(x) compared to f(x) = 4x + 2 Shift up 8 Shift left 6 September 27th

  2. Match the Equation to the Translation G(x) = 2x - 4 • g(x)=2x -8 • g(x)= 2(x+5)-4 • g(x)=2x + 8 • g(x)=2(x-4) - 6 • Shift up 4 units • Shift down 4 units • Shift right 4 and down 2 • Shift left 5

  3. Horizontal, vertical, or both?!

  4. Homework Answers

  5. What has changed?!

  6. Part II-Transformations Stretches & Compressions

  7. 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.

  8. Stretch vs. Compression • Stretches=pull away from y axis • Compression=pulled toward the y axis

  9. Horizontal vs. Vertical • Horizontal=x changes • Vertical=y changes

  10. Stretches and compressions are not congruent to the original graph. They will have different rates of change! Stretches and Compressions

  11. #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

  12. #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

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

  14. Writing New Compressions and Stretches

  15. #1 .

  16. # 2

  17. # 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. .

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