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Daily Check

Daily Check. Graph the following equations. Math II. UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s Question: How are absolute value equations similar to piecewise functions? Standard: MM2A1.a,b.

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Daily Check

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  1. Daily Check Graph the following equations.

  2. Math II UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s Question: How are absolute value equations similar to piecewise functions? Standard: MM2A1.a,b

  3. Absolute Value as Piecewise Functions Section 2.5

  4. Piecewise Functions • Piecewise functions are functions that can be represented by more than one equation, with each equation corresponding to a different part of the domain. • Piecewise functions do not always have to be line segments. The “pieces” could be pieces of any type of graph. • This type of function is often used to represent real-life problems like ticket prices.

  5. Example x + 1, if x < 1 2, if 1 ≤ x ≤ 3 (x-3)2 + 2, if x > 3 f (x) =

  6. Absolute Value as Piecewise • We usually write an absolute value function as f (x)= x , but since absolute value is a measure of distance and distance is always positive, it also can be written as follows: -x, if x < 0 x, if x ≥ 0 f (x) =

  7. Writing Abs. Value as Piecewise • For I x – h I ≥ 0, simplify the equation given by distributing and combining like terms. • For I x – h I < 0, substitute –(x – h) in place of I x - h I. Then, simplify.

  8. Example • Write y = 2 Ix – 4I – 10 as a piecewise function. • For (x-4) ≥ 0 2(x – 4) – 10 = 2x – 8 – 10 = 2x – 18 (when x ≥ 4) • For (x-4) < 0 2[-(x-4)] – 10 = 2(-x + 4) – 10 = -2x + 8 – 10 = -2x – 2 (when x < 4))

  9. Graphs of Both y=-2x-2 y=2x-18

  10. EOCT Practice A

  11. EOCT Practice C

  12. Writing Abs. Value as Piecewise • Using a graph

  13. Writing Abs. Value as Piecewise • Try this one...

  14. Practice • Worksheet

  15. Homework • Worksheet

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