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2.7 Piecewise Functions

Learn how piecewise functions can represent real-life situations with different equations for different parts of the domain. Evaluate f(x) for x = 0, x = 2, and x = 4 using the appropriate equations.

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2.7 Piecewise Functions

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  1. 2.7 Piecewise Functions p. 114

  2. In real life functions are represented by a combination of equations, each corresponding to a part of the domain. • These are called piecewise functions.

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

  4. 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

  5. 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)

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

  7. Graph:

  8. Step Functions

  9. Graph :

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