# Writing absolute value functions as piecewise equations

A General Note: Piecewise Functions A piecewise function is a function in which more than one formula is used to define the output. It is the distance from 0 on the number line. More examples of Step Functions: NOTE: The re-posting of materials in part or whole from this site to the Internet is copyright violation and is not considered "fair use" for educators.

Each formula has its own domain, and the domain of the function is the union of all these smaller domains.

Try It Graph the following piecewise function. Absolute Value Graphs Warm-Up.

### Graphing absolute value piecewise functions

One of the most famous step functions is the Greatest Integer Function. In essence, the greatest integer function rounds down a real number to the nearest integer. A step function is discontinuous not continuous. What do you need to know or remember in order to tackle this question? Example: Graphing a Piecewise Function Sketch a graph of the function. Problem 3 is a preview today's investigation. The function is constant in each interval. 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. Identify the intervals for which different rules apply. More examples of Step Functions: NOTE: The re-posting of materials in part or whole from this site to the Internet is copyright violation and is not considered "fair use" for educators. This example is a function. All of these definitions require the output to be greater than or equal to 0. The assessment includes a lot of graphs so that students are motivated to consider shortcuts for creating graphs and writing piecewise functions to match the graphs. Look for and make use of structure. What is another option?

As students work I make observations to help me decide how to proceed with the investigation. 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.

Determine formulas that describe how to calculate an output from an input in each interval. When they make this connection, they will be able to reason about and visualize absolute value functions more efficiently MP7. 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.

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

## Graphing absolute value piecewise functions

What do you need to know or remember in order to tackle this question? The function is constant in each interval. Example: Graphing a Piecewise Function Sketch a graph of the function. If we input 0, or a positive value, the output is the same as the input. A piecewise function is a function in which more than one formula is used to define the output over different pieces of the domain. It is the distance from 0 on the number line. Watch this tutorial video to learn how. For help with greatest integer functions on your calculator, Click Here! Sometimes, we come across a function that requires more than one formula in order to obtain the given output. Do not graph two functions over one interval because it would violate the criteria of a function. The questions also show different transformations of the function. Each value corresponds to one equation in a piecewise formula.

Graphing Absolute Value Functions Example. When you offer help always connect absolute value back to distance.

### How to write a piecewise function

Use braces and if-statements to write the function. 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 assessment includes a lot of graphs so that students are motivated to consider shortcuts for creating graphs and writing piecewise functions to match the graphs. Show Solution To find the cost of using 1. For help with greatest integer functions on your calculator, Click Here! Graph the following piecewise function with an online graphing tool. A piecewise function is a function in which more than one formula is used to define the output over different pieces of the domain. I will use this information to decide which resource to use in the investigation. Graph piecewise-defined functions. This example is a function.

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