Evaluating 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 at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which interval the point falls into and then use the corresponding expression to find the function's value.

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 if a function is defined for all real numbers?

Back

If a function is defined for all real numbers, it means that there are no restrictions on the input values, and the domain is (-∞, +∞).

Front

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

Back

To find the value of a piecewise function at a given point, identify the correct piece of the function that corresponds to that point and substitute the point into that piece.

Front

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

Back

Endpoints in a piecewise function indicate where the function changes from one expression to another, and they can be included or excluded from the domain.

Front

What is the notation used for piecewise functions?

Back

Piecewise functions are typically written using curly braces, with each piece defined for a specific interval, e.g., f(x) = { expression1 for x < a, expression2 for a ≥ a }.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval, ensuring to use open or closed dots at endpoints based on inclusion.

Front

What is the value of f(-3) if f(x) is defined piecewise?

Back

To find f(-3), identify which piece of the piecewise function applies to x = -3 and evaluate that expression.

Front

What is the value of f(2) if f(x) is defined piecewise?

Back

To find f(2), determine which piece of the piecewise function applies to x = 2 and evaluate that expression.