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

How do you denote a piecewise function?

Back

A piecewise function is denoted using curly braces, with each piece of the function defined for specific intervals of the input variable.

Front

What is the domain of a function?

Back

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

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

How do you find the value of a piecewise function at a specific point?

Back

To find the value of a piecewise function at a specific point, determine which piece of the function applies to that input value and then evaluate the expression.

Front

What does 'x < 4' mean in a piecewise function?

Back

It means that the corresponding expression applies to all values of x that are less than 4.

Front

What does 'x ≥ 4' mean in a piecewise function?

Back

It means that the corresponding expression applies to all values of x that are greater than or equal to 4.

Front

If f(x) = { x if x < 4; -x + 1 if x ≥ 4, what is f(3)?

Back

f(3) = 3, since 3 < 4.

Front

If f(x) = { -x + 1 if x < 4; x if x ≥ 4, what is f(5)?

Back

f(5) = 5, since 5 ≥ 4.

Front

What is the significance of the domain restriction in a piecewise function?

Back

Domain restrictions indicate the values for which the function is valid and help to define the behavior of the function.