Piecewise Functions
Math ⇒ Functions
Piecewise Functions starts at 10 and continues till grade 12.
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See sample questions for grade 10
Describe a real-life situation that can be modeled by a piecewise function.
Describe how to determine which piece of a piecewise function to use for a given value of x.
What is a piecewise function?
Write a piecewise function that equals 0 for x < 0, 1 for 0 ≤ x < 1, and 2 for x ≥ 1.
Write a piecewise function that equals 5 for x ≤ -1, 0 for -1 < x < 1, and -5 for x ≥ 1.
Write a piecewise function that equals x² for x < 2 and 3x for x ≥ 2.
Given f(x) = { x+2 for x < 1, 4 for x = 1, 2x for x > 1 }, is f(x) continuous at x = 1?
Which of the following values of x will use the second piece in the function f(x) = { x² for x < 1, 2x+1 for x ≥ 1 }? (1) x = 0, (2) x = 1, (3) x = -2, (4) x = 0.5
Which of the following is a piecewise function? (1) f(x) = 2x + 1, (2) f(x) = |x|, (3) f(x) = x² for x < 0, f(x) = x for x ≥ 0, (4) f(x) = 3
Which of the following is NOT a piecewise function? (1) f(x) = x³, (2) f(x) = { x+1 for x < 0, x-1 for x ≥ 0 }, (3) f(x) = |x|, (4) f(x) = { 2 for x < 1, 3 for x ≥ 1 }
Which of the following is the correct piecewise definition for the sign function? (1) f(x) = 1 for x > 0, 0 for x = 0, -1 for x < 0, (2) f(x) = x, (3) f(x) = |x|, (4) f(x) = x²
Which of the following is the correct piecewise definition of the greatest integer function? (1) f(x) = x, (2) f(x) = the largest integer less than or equal to x, (3) f(x) = x², (4) f(x) = x+1
Fill in the blank: For the function f(x) = { 2x for x ≤ 1, x+3 for x > 1 }, the value of f(1) is _______.
Fill in the blank: For the function f(x) = { 3x for x < 0, 2 for x ≥ 0 }, the value of f(-2) is _______.
Fill in the blank: For the function f(x) = { x for x < 1, 2 for x ≥ 1 }, the value of f(0.5) is _______.
Fill in the blank: For the function f(x) = { x+1 for x < 3, 2x for x ≥ 3 }, the value of f(4) is _______.
Given f(x) = { x+2 for x < 1, 4 for x = 1, 2x for x > 1 }, is f(x) continuous at x = 1?
True or False: A piecewise function can be discontinuous at some points.
True or False: A piecewise function can have more than two pieces.
True or False: Every function can be written as a piecewise function.
