Piecewise Functions With Domain and Range

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 the domain.

Front

How do you determine 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, often expressed in interval notation.

Front

What is the range of a function?

Back

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

Front

How do you find the range of a piecewise function?

Back

To find the range of a piecewise function, evaluate each piece of the function over its domain and combine the resulting output values.

Front

What does the notation 'x > 3' indicate in a piecewise function?

Back

The notation 'x > 3' indicates that the corresponding expression applies only to values of x that are greater than 3.

Front

What does the notation 'x ≤ 0' indicate in a piecewise function?

Back

The notation 'x ≤ 0' indicates that the corresponding expression applies only to values of x that are less than or equal to 0.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on the same set of axes, ensuring to use open or closed circles to indicate whether endpoints are included.

Front

What is the significance of the endpoints in a piecewise function?

Back

Endpoints in a piecewise function indicate where one piece of the function transitions to another, and whether those points are included in the domain.

Front

What is the equation of the piece for x ≤ 0 in the provided example?

Back

The equation of the piece for x ≤ 0 is f(x) = x - 2.

Front

What is the equation of the piece for x > 3 in the provided example?

Back

The equation of the piece for x > 3 is f(x) = 2x + 3.