Piecewise Functions- Alg 2B

Front

Define a piecewise function.

Back

A piecewise function is a function that is defined by different expressions or formulas for different intervals of its domain.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x-values) for which the function is defined, which may vary across different pieces.

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which interval the point falls into and use the corresponding expression to find the function's value.

Front

What is the significance of the notation f(x) in piecewise functions?

Back

The notation f(x) represents the output of the function for a given input x, which may depend on the specific piece of the function applicable to that input.

Front

Evaluate the piecewise function f(x) = { 2x + 1, x < 0; x^2, 0 ≤ x < 3; 4, x ≥ 3 } at x = 2.

Back

f(2) = 2^2 = 4.

Front

What is the value of f(0) for the piecewise function f(x) = { 2x + 1, x < 0; x^2, 0 ≤ x < 3; 4, x ≥ 3 }?

Back

f(0) = 0^2 = 0.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval, ensuring to use open or closed circles to indicate whether endpoints are included.

Front

What is the value of f(12) for the piecewise function f(x) = { 2x + 1, x < 0; x^2, 0 ≤ x < 3; 4, x ≥ 3 }?

Back

f(12) = 4.

Front

Evaluate f(-2) for the piecewise function f(x) = { 2x + 1, x < 0; x^2, 0 ≤ x < 3; 4, x ≥ 3 }.

Back

f(-2) = 2(-2) + 1 = -4 + 1 = -3.

Front

What does it mean for a piecewise function to be continuous?

Back

A piecewise function is continuous if there are no breaks, jumps, or holes in the graph, meaning the function's value approaches the same limit from both sides at the boundaries of the pieces.