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 domain of a piecewise function?

Back

To determine the domain, identify the intervals for which each piece of the function is defined and combine them.

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 range of a piecewise function?

Back

To find the range, evaluate each piece of the function and determine the minimum and maximum output values.

Front

What does DNE stand for in mathematics?

Back

DNE stands for 'Does Not Exist', indicating that a certain value or limit cannot be defined.

Front

What is the significance of the notation [ ] in interval notation?

Back

The notation [ ] indicates that the endpoint is included in the interval, meaning the value is part of the set.

Front

What does the notation ( ) signify in interval notation?

Back

The notation ( ) indicates that the endpoint is not included in the interval, meaning the value is not part of the set.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval and ensure to use open or closed dots as appropriate.

Front

What is the formula for a linear function?

Back

The formula for a linear function is typically written as f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).