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 determine the value of a piecewise function at a specific point?

Back

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

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 does it mean for a function to be defined at a point?

Back

A function is defined at a point if there is a corresponding output value (y-value) for that input value (x-value).

Front

If f(x) = x + 2 for x ≤ 0, what is f(-3)?

Back

f(-3) = -3 + 2 = -1.

Front

If f(x) = 4x for x > 0, what is f(2)?

Back

f(2) = 4(2) = 8.

Front

What is the significance of the domain restrictions in piecewise functions?

Back

Domain restrictions indicate the specific intervals over which each piece of the function is applicable.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval and ensure to use open or closed circles to indicate whether endpoints are included.

Front

What is the value of f(x) when x = 2 in the function defined as f(x) = { 0, x < 1; 4, x ≥ 1 }?

Back

f(2) = 4.

Front

What does it mean for a function to not exist at a certain point?

Back

A function does not exist at a certain point if there is no defined output value for that input value.