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Piecewise Functions

Piecewise Functions. A piecewise function is a function that has different rules for its different parts. Example:

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Piecewise Functions

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  1. Piecewise Functions A piecewise function is a function that has different rules for its different parts. Example: ExFed charges $4.00 to mail packages weighing up to 6 lbs. For packages weighing between 6 and 8 lbs, the charge is $4 plus $0.50 per pound, and packages 8 pounds or heavier are charged $3 and $1 per pound. Write a piecewise function to determine the cost, in dollars, c(x), of mailing a package weighing x pounds. Function for packages up to 6 lbs: c(x) = 4

  2. Piecewise Functions A piecewise function is a function that has different rules for its different parts. Example: ExFed charges $4.00 to mail packages weighing up to 6 lbs. For packages weighing between 6 and 8 lbs, the charge is $4 plus $0.50 per pound, and packages 8 pounds or heavier are charged $3 and $1 per pound. Write a piecewise function to determine the cost, in dollars, c(x), of mailing a package weighing x pounds. Function for packages between 6 and 8 lbs: c(x) = 0.5x + 4

  3. Piecewise Functions A piecewise function is a function that has different rules for its different parts. Example: ExFed charges $4.00 to mail packages weighing up to 6 lbs. For packages weighing between 6 and 8 lbs, the charge is $4 plus $0.50 per pound, and packages 8 pounds or heavier are charged $3 and $1 per pound. Write a piecewise function to determine the cost, in dollars, c(x), of mailing a package weighing x pounds. Function for packages greater than or equal to 8 lbs: c(x) = x + 3

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  5. Piecewise Functions A copy shop charges $0.15 per photocopy for orders of 20 or fewer photocopies, $0.12 per photocopy for orders of 50 or fewer but more than 20 photocopies, and $0.10 per photocopy for orders of more than 50 photocopies. Write and graph a piecewise function to represents the cost C  in dollars for x number of photocopies. Function for ≤ 20 copies: C = 0.15x Function for > 20 but ≤ 50 copies: C = 0.12x Function for > 50 copies: C = 0.10x

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  8. Writing Piecewise Functions If you were given the graph, could you write the piecewise function?

  9. Writing Piecewise Functions This function has 2 parts:

  10. Piecewise Functions One part when x is… less than zero,

  11. Piecewise Functions And one part when x is… greater than or equal to zero. **Alternatively: x ≤ 0 & x > 0

  12. Piecewise Functions The equation of the part that is less than zero can be found by calculating the… Slope = -1 y-int. = (0,0) Equation: y = -x

  13. Piecewise Functions The equation of the part that is greater than or equal to zero can be found by calculating the … Slope = 1 y-int. = (0,0) Equation: y = x

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  16. Piecewise Functions Notice we can also write the function rule of this graph as…

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