Evaluate piecewise functions

Front

What is 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

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 value of f(0) if f(x) = { 2x + 4, x < 0; 4, x = 0; x^2 - 1, x > 0 }?

Back

4

Front

Evaluate f(6) for the piecewise function f(x) = { -5, x < 0; 7, x = 6; 2, x > 6 }.

Back

7

Front

What is g(-2) if g(x) = { -7, x < -1; 7, -1 ≤ x < 2; 1, x ≥ 2 }?

Back

7

Front

Find f(-2) if f(x) = { -3, x < -2; 8, -2 ≤ x < 1; 6, x ≥ 1 }.

Back

8

Front

What is f(-1) if f(x) = { 6, x < -1; -2, -1 ≤ x < 0; 0, x ≥ 0 }?

Back

-2

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) for which the function is defined, which may vary across different pieces.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval, ensuring to use open or closed dots based on whether the endpoints are included.

Front

What does it mean if a piecewise function has a discontinuity?

Back

A discontinuity in a piecewise function occurs when there is a jump or break in the graph, indicating that the function is not continuous at that point.