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?

Back

To evaluate a piecewise function, identify the interval in which the input value falls and use the corresponding expression to find the output.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points in that interval, the function's value at the second point is greater than at the first point.

Front

What is the notation for an open interval?

Back

An open interval is denoted as (a, b), meaning it includes all numbers between a and b, but not a and b themselves.

Front

What is the notation for a closed interval?

Back

A closed interval is denoted as [a, b], meaning it includes all numbers between a and b, including a and b.

Front

What is the value of f(2) if f(x) = { -3 for x < 0, 2x for 0 ≤ x < 5, 10 for x ≥ 5 }?

Back

f(2) = 4.

Front

What is the value of f(33) if f(x) = { -3 for x < 0, 2x for 0 ≤ x < 5, 10 for x ≥ 5 }?

Back

f(33) = 6.

Front

How do you find the domain of a piecewise function?

Back

The domain of a piecewise function is the union of the domains of each piece defined in the function.

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values from the function.

Front

What does DNE stand for in function evaluation?

Back

DNE stands for 'Does Not Exist', indicating that the function does not have a value for that input.