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Warm Up:

Graph the following equations: 1) y = -3x + 2 2) y = ½ x – 3 3) 3y = 2x + 6. Warm Up:. 2.0A Notes (Section 1.1 in Textbook). Function families and their transformations. Parent Functions. What is the parent function?.

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Warm Up:

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  1. Graph the following equations: • 1) y = -3x + 2 2) y = ½ x – 3 • 3) 3y = 2x + 6 Warm Up:

  2. 2.0A Notes (Section 1.1 in Textbook) Function families and their transformations

  3. Parent Functions

  4. What is the parent function?

  5. A Translation happens when you see an addition or subtraction sign. • If the +/- is in parenthesis with the “x”, the graph moves left or right, OPPOSITE the sign in the parenthesis! (horizontal translation) • If the +/- is not in parenthesis with the “x”, the graph moves up or down (vertical translation). What is a translation?

  6. Exploration: Graph the following on the same grid with different colors. • 1) y = x2 • 2) y = x2 + 4 4) y = (x + 4)2 • 3) y = x2 – 2 5) y = (x – 2)2 Where did graph #1 “go” in each of the following problems?

  7. Graph g(x) = x – 4. List the parent function and describe what transformation occurred.

  8. 1) y = x • 2) y = 6x • 3) y = x Let’s explore: Compare the three graphs

  9. 1) y = x2 • 2) y = 4x2 • 3) y = x2 Let’s Explore: Compare the three graphs

  10. 1) y = • 2) y = 9 • 3) y = Let’s explore: Compare the three graphs

  11. Rule: • If you multiply by a number greater than one, the graph with become “steeper” (stretch) • If you multiply by a number between zero and one (a fraction), the graph will become “shallower” (shrink)

  12. What about these? • 1) y = x • 2) y = -x • 3) y = x2 • 4) y = -x2 • 5) y = • 6) y = - Let’s explore: Compare the sets of graphs

  13. These are reflections (mirroring, flipping). They reflect or flip over the x axis.

  14. 1) y = -3x 2) f(x)= 3) y = -(x – 4)2 - 1 • 4) f(x)= (x + 1)- 4 5) y = 6) f(x) = 5(x – 2)2 - 7 Describe the transformations

  15. A reflection is noted with a negative sign in front of the x variable. The graph is either reflected, or flipped, over the x-axis or y-axis.

  16. Look at the table, what is the main change?

  17. Given f(x) = -x, answer the following: • 1) What is the parent function? • 2) What does the graph of the parent function look like? • 3) What does the graph of f(x) = -x look like?\ • 4) Describe the transformation that occurred.

  18. You try!

  19. When you multiply the parent function by a number greater than one, it is a stretch. • When you multiply the parent function by a number less than one, it is a shrink. • Stretch: Shrink: What is a stretch or a shrink?

  20. You try!

  21. Warm up Friday

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