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Daily Check

Daily Check. Solve and graph the following equations. 1. . 2. Math II. UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s Question: How do we graph piecewise functions? Standard: MM2A1.a,b. 2.5 Piecewise Functions .

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Daily Check

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  1. Daily Check Solve and graph the following equations. 1. 2.

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

  3. 2.5 Piecewise Functions

  4. Up to now, we’ve been looking at functions represented by a single equation. • In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain. • These are called piecewise functions.

  5. One equation gives the value of f(x) when x ≤ 1 • And the other when x>1

  6. Evaluate f(x) when x=0, x=2, x=4 • First you have to figure out which equation to use • You NEVER use both X=4 X=2 X=0 This one fits Into the top equation So: 2(4) + 1 = 9 f(4) = 9 So: 0+2=2 f(0)=2 This one fits here So: 2(2) + 1 = 5 f(2) = 5 This one fits here

  7. Graph: • For all x’s < 1, use the top graph (to the left of 1) • For all x’s ≥ 1, use the bottom graph (to the • right of 1)

  8. x=1 is the breaking point of the graph. To the left is the top equation. To the right is the bottom equation.

  9. Graph: Point of Discontinuity

  10. Step Functions

  11. Graph :

  12. Special Step Functions Two particular kinds of step functions are called ceiling functions ( f (x)= and floor functions ( f (x)= ). In a ceiling function, all nonintegers are rounded up to the nearest integer. An example of a ceiling function is when a phone service company charges by the number of minutes used and always rounds up to the nearest integer of minutes.

  13. Special Step Functions In a floor function, all nonintegers are rounded down to the nearest integer. The way we usually count our age is an example of a floor function since we round our age down to the nearest year and do not add a year to our age until we have passed our birthday. The floor function is the same thing as the greatest integer function which can be written as f (x)=[x].

  14. Class work Textbook pg. 51 #1-8

  15. HW Assignment Textbook p. 52 #1-6; and p. 53 #26

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