Piecewise Functions
Math ⇒ Functions
Piecewise Functions starts at 10 and continues till grade 12.
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Describe a real-world situation that could be modeled by a piecewise function.
Given f(x) = { 3x+2, if x < 1; 5, if x = 1; 2x-1, if x > 1 }, find all values of x where f(x) = 5.
Given the function f(x) = { x+1, if x ≤ 2; 3x-4, if x > 2 }, for which value of x does f(x) switch from one rule to another?
If f(x) = { x+1, if x < 2; 2x-3, if x ≥ 2 }, for which value of x is f(x) = 5?
If f(x) = { x+2, if x < 0; 2x-1, if x ≥ 0 }, what is the range of f(x)?
What is a piecewise function?
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).
Describe a real-world situation that could be modeled by a piecewise function.
Fill in the blank: The function f(x) = { x², if x < 1; ___, if x ≥ 1 } is continuous at x = 1 if the blank is filled with _______.
Which of the following is a correct definition of a piecewise linear function? (1) A function made up of straight line segments, (2) A function made up of parabolas, (3) A function made up of circles, (4) A function made up of sines and cosines
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) All of the above
Which of the following is a reason a function might be defined piecewise? (1) To model real-world situations with different rules, (2) To make the function continuous, (3) To make the function differentiable, (4) None of the above
Which of the following is NOT a piecewise function? (1) f(x) = x², (2) f(x) = {x+1, x<0; x-1, x≥0}, (3) f(x) = |x|, (4) f(x) = {2x, x<1; 3x, x≥1}
Fill in the blank: The function f(x) = { x², 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) = { x², if x < 1; ___, if x ≥ 1 } is differentiable at x = 1 if the blank is filled with _______.
Given f(x) = { x+2, if x < 0; 2x-1, if x ≥ 0 }, is f(x) continuous at x = 0?
If f(x) = { x², if x < 1; 2x-1, if x ≥ 1 }, is f(x) continuous at x = 1?
If f(x) = { x², if x ≤ 2; 4x-4, if x > 2 }, is f(x) continuous at x = 2?
If f(x) = { x², if x ≤ 2; 4x-4, if x > 2 }, is f(x) differentiable at x = 2?
