# Write a piecewise function for each graph

Watch this tutorial video to learn how. With a domain of all real numbers and a range of values greater than or equal to 0, absolute value can be defined as the magnitude, or modulus, of a real number value regardless of sign.

### How to write a piecewise function from a word problem

Identify the intervals for which different rules apply. Use braces and if-statements to write the function. Do not graph two functions over one interval because it would violate the criteria of a function. A step function is discontinuous not continuous. Average rate of change: is constant on each straight line section ray of the graph. Provided by: OpenStax. Try It 8 Graph the following piecewise function. Determine formulas that describe how to calculate an output from an input in each interval. Each formula has its own domain, and the domain of the function is the union of all these smaller domains. Read more about Absolute Value.

At the endpoints of the domain, we draw open circles to indicate where the endpoint is not included because of a less-than or greater-than inequality; we draw a closed circle where the endpoint is included because of a less-than-or-equal-to or greater-than-or-equal-to inequality.

The constant pieces are observed across the adjacent intervals of the function, as they change value from one interval to the next.

We plot the graphs for the different formulas on a common set of axes, making sure each formula is applied on its proper domain. Each value corresponds to one equation in a piecewise formula.

A General Note: Piecewise Functions A piecewise function is a function in which more than one formula is used to define the output. Each value corresponds to one equation in a piecewise formula.

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