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2.8 Absolute Value functions

2.8 Absolute Value functions. In this lesson you will :. Represent absolute value functions. Use absolute value function to model real-life situations. Warm-up. The definition of Absolute Value. By the way…..is x a positive or negative number?. Let’s graph y = |x|. x if x > 0.

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2.8 Absolute Value functions

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  1. 2.8 Absolute Value functions

  2. In this lesson you will: • Represent absolute value functions. • Use absolute value function to model real-life situations.

  3. Warm-up

  4. The definition of Absolute Value By the way…..is x a positive or negative number?

  5. Let’s graph y = |x| x if x > 0 0 if x = 0 |x|= -x if x < 0 Vertex Notice that the graph is symmetric in the y axis because for every point (x,y) there is a corresponding point (-x,y)

  6. Let’s explore the graphy = a|x-h|+k • The graph has a vertex (h,k) and is symmetric in the line x=h. • The graph is V-shaped. It opens up if a>0 and down if a<0. • The graph is wider then the graph of y=|x| if |a|<1. • The graph is narrower that the graph of y=|x| if |a|>1.

  7. Does the graph open “up” or “down”? What are the coordinates of the vertex?

  8. Does the graph open “up” or “down”? What are the coordinates of the vertex?

  9. Graph this function

  10. Graph this function Why is the graph narrower than the last one?

  11. Write an equation for this graph y = 2|x-3|+1

  12. Write an equation for this graph y = -|x+2|+3

  13. Homework12-17 all, 19-39 odd, 44-46 all

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