3.2 Evaluate 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 does f(0) = -2 indicate in a piecewise function?

Back

It indicates that when the input (x) is 0, the output (f(x)) is -2, based on the definition of the function for that interval.

Front

If f(-2) = 4, what does this tell us about the function at x = -2?

Back

It tells us that the output of the function is 4 when the input is -2, indicating the specific value of the function at that point.

Front

What is the significance of undefined values in piecewise functions?

Back

Undefined values indicate that the function does not have a valid output for certain inputs, often due to discontinuities or restrictions in the function's definition.

Front

How can you determine the output of f(1) = 2 in a piecewise function?

Back

You determine the output by identifying the correct piece of the function that applies when x = 1, which gives the output of 2.

Front

What does f(4) = 7 imply about the function's behavior at x = 4?

Back

It implies that the function has a defined value of 7 at x = 4, indicating continuity or a specific output at that point.

Front

What does it mean if f(8) = 2 in a piecewise function?

Back

It means that for the input x = 8, the function outputs a value of 2, based on the relevant piece of the function.

Front

What is the general form of a piecewise function?

Back

The general form of a piecewise function is: f(x) = { expression1 for x in interval1, expression2 for x in interval2, ... }.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval, ensuring to use open or closed circles to indicate whether endpoints are included.