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 parts of its domain.

Front

What are the domain restrictions for the middle piece of a piecewise function?

Back

Domain restrictions specify the values of x for which a particular piece of the function is applicable.

Front

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

Back

To evaluate a piecewise function at a specific point, determine which piece of the function applies to that point based on its domain.

Front

What is the significance of the domain in piecewise functions?

Back

The domain determines the intervals over which each piece of the function is valid.

Front

If f(x) = { x^2 for x < 0, 2x for 0 ≤ x < 3, 3 for x ≥ 3 }, what is f(2)?

Back

f(2) = 4 (since 2 is in the interval 0 ≤ x < 3, we use 2x).

Front

What is the output of a piecewise function if the input is outside its defined domain?

Back

The output is undefined for inputs outside the defined domain of the piecewise function.

Front

How do you find the value of h(5) in a piecewise function?

Back

Identify which piece of the function applies to x = 5 and substitute 5 into that piece.

Front

Evaluate f(3) for the piecewise function f(x) = { x - 1 for x < 3, x + 1 for x ≥ 3 }.

Back

f(3) = 4 (since 3 is in the interval x ≥ 3, we use x + 1).

Front

What does it mean if a piecewise function has a gap in its graph?

Back

A gap indicates that there is a value in the domain that does not have a corresponding output in the function.

Front

If f(x) = { 2x + 1 for x < 1, 3 for 1 ≤ x < 4, x - 2 for x ≥ 4 }, what is f(-2)?

Back

f(-2) = -3 (since -2 is in the interval x < 1, we use 2x + 1).