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Piecewise Functions

Math ⇒ Functions

Piecewise Functions starts at 10 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Piecewise Functions. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.
See sample questions for grade 11
Describe a real-world situation that can be modeled by a piecewise function.
Describe how to determine if a piecewise function is continuous at a point where the formula changes.
Explain why the function f(x) = { x², if x < 0; x, if x ≥ 0 } is not differentiable at x = 0.
Given f(x) = { 2x+1, if x < 0; 3x-2, if x ≥ 0 }, for which value of x does f(x) = 4?
If f(x) = { x+1, if x < 0; 0, if x = 0; x-1, if x > 0 }, what is the range of f(x)?
A function is defined as f(x) = { 2x+1, if x ≤ 0; x², if x > 0 }. Find f(0).
A function is defined as f(x) = { 2x+1, if x ≤ 0; x², if x > 0 }. Find f(3).
Explain why the function f(x) = { x², if x < 0; x, if x ≥ 0 } is not differentiable at x = 0.
Fill in the blank: The domain of the piecewise function f(x) = { x+1, if x < 0; x², if x ≥ 0 } is _______.
Which of the following is a correct way to write a piecewise function? (1) f(x) = x+1 for all x, (2) f(x) = { x+1, if x < 0; x-1, if x ≥ 0 }, (3) f(x) = x², (4) f(x) = x-1 for all x
Which of the following is a possible graph of a piecewise function? (1) A straight line, (2) Two lines joined at a point, (3) A parabola, (4) A circle
Which of the following is NOT a piecewise function? (1) f(x) = x², (2) f(x) = {x+1, if x<0; x-1, if x≥0}, (3) f(x) = |x|, (4) f(x) = {2x, if x<1; 3, if x≥1}
Which of the following is the correct piecewise definition of the greatest integer function (floor function)? (1) f(x) = x, (2) f(x) = the largest integer less than or equal to x, (3) f(x) = {x, if x is integer; x-1, if x is not integer}, (4) f(x) = x+1
Fill in the blank: The domain of the piecewise function f(x) = { x+1, if x < 0; x², if x ≥ 0 } is _______.
Fill in the blank: The function f(x) = { x, if x < 1; ___, if x ≥ 1 } is continuous at x = 1 if the blank is filled with _______.
Fill in the blank: The function f(x) = { x+1, if x < 0; ___, if x ≥ 0 } is continuous at x = 0 if the blank is filled with _______.
Given f(x) = { 2x+1, if x < 1; 5, if x = 1; x², if x > 1 }, is f(x) continuous at x = 1?
Given f(x) = { x², if x < 1; 2x, if x ≥ 1 }, is f(x) continuous at x = 1?
Given f(x) = { x², if x < 1; 2x-1, if x ≥ 1 }, is f(x) continuous at x = 1?
True or False: A piecewise function can have more than two pieces.