Piecewise/Step 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 for that interval.

Front

What is the greatest integer function?

Back

The greatest integer function, denoted as ⌊x⌋, is a piecewise function that returns the largest integer less than or equal to x.

Front

What does the notation f(x) mean in the context of functions?

Back

f(x) represents the output of the function f for a given input x.

Front

How can 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 circles to indicate whether endpoints are included.

Front

What is the slope-intercept form of a linear function?

Back

The slope-intercept form of a linear function is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the value of a piecewise function at a negative input?

Back

Identify the interval that includes the negative input and apply the corresponding expression for that interval.

Front

What is the significance of the red portion in a piecewise function graph?

Back

The red portion typically indicates a specific segment of the piecewise function that is being highlighted or analyzed.

Front

How do you determine the output of a function at a specific input?

Back

Substitute the input value into the function's expression and simplify to find the output.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values for which the function is defined.