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Absolute Value Graphs

Absolute Value Graphs. Mrs. King Unit 9, Day 1. Recall…. Absolute Value: the distance that a number is from zero on the number line. Examples:. Find each absolute value. a. |–2.5|. b. |7|. –2.5 is 2.5 units from 0 on a number line. 7 is 7 units from 0 on a number line. |–2.5| = 2.5.

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Absolute Value Graphs

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  1. Absolute Value Graphs Mrs. King Unit 9, Day 1

  2. Recall… • Absolute Value: the distance that a number is from zero on the number line

  3. Examples: Find each absolute value. a. |–2.5| b. |7| –2.5 is 2.5 units from 0 on a number line. 7 is 7 units from 0 on a number line. |–2.5| = 2.5 |7| = 7

  4. New Terminology: • An absolute-value function is a function whose rule contains an absolute-value expression.

  5. What does the graph of y = |x| look like?

  6. The absolute value function always makes a ‘V’ shape graph.

  7. Vocabulary • The lowest point on the graph of an absolute value function is called the vertex. • An axis of symmetry of the graph of a function is a vertical line that divides the graph into mirror images.

  8. Absolute Value Function • Vertex • Axis of Symmetry

  9. Vocabulary • A transformation changes a graph’s size, shape, position, or orientation. • A translation is a transformation that shifts a graph horizontally and/or vertically, but does not change its size, shape, or orientation.

  10. Try Graphing These Absolute Value Functions Do you notice any patterns?

  11. Try Graphing These Absolute Value Functions Vertical Translation: f(x) + k shifts up f(x) - k shifts down Using your rule, sketch the following problems.

  12. Write an equation for each graph.

  13. Try Graphing These Absolute Value Functions Do you notice any patterns?

  14. Try Graphing These Absolute Value Functions Horizontal Translation: f(x - h) shifts to the right f(x + h) shifts to the left Using your rule, sketch the following problems.

  15. Write an equation for each graph.

  16. Lesson Wrap Up:

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