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 does the domain of a function represent?

Back

The domain of a function represents all the possible input values (x-values) for which the function is defined.

Front

How do you determine the domain of a piecewise function?

Back

To determine the domain of a piecewise function, identify the intervals for which each piece of the function is defined and combine them.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph.

Front

What is the difference between an open interval and a closed interval?

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.

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 input value and use the corresponding formula.

Front

What is the significance of the notation f(x)?

Back

The notation f(x) represents the output of the function f for a given input x.

Front

What is a function's output when x = 2 in the piecewise function defined as: f(x) = { x + 1 for x < 2; 3 for x ≥ 2 }?

Back

f(2) = 3.

Front

What is a function's output when x = 0 in the piecewise function defined as: f(x) = { 2x for x < 1; x^2 for x ≥ 1 }?

Back

f(0) = 0.