# Writing absolute value functions as piecewise equations

A dialogue might proceed as follows: The questions also show different transformations of the function. Eventually, I expect students to "invent" or use the idea of a vertex for the absolute value function.

You plan to sell She Love Math t-shirts as a fundraiser. The way that I facilitate this investigation depends on how students engage with the Warm-up. So the whole piecewise function is: Piecewise Function Word Problems Problem: Look for and make use of structure.

Problem 2 will challenge students. We have to start at 0, since dogs have to weigh over 0 pounds: And, even better, a site that covers math topics from before kindergarten through high school.

As students work I make observations to help me decide how to proceed with the investigation. Here are more examples, with explanations. What is another option? What do you need to know or remember in order to tackle this question? It can be helpful to have a reference poster showing a sample problem about continuity on the board, so if there is a student who is interested in making one of these posters, they can use this as a piece of portfolio evidence at the end of the unit.

Write a function that models this situation. If you choose to use this resource, you can ask students to write function rules for each of the graphs they create using either absolute value functions or piecewise functions.

The piecewise function is: To review how to obtain equations from linear graphs, see Obtaining the Equations of a Line, and from quadratics, see Finding a Quadratic Equation from Points or a Graph. You might want to review Quadratic Inequalities for the second example below: What could you do about that?

When you offer help always connect absolute value back to distance. You may also be asked to take an absolute value graph and write it as a piecewise function: 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.

Problem 1 will likely require students to get out some notes or reference materials, so if they struggle to start, ask them: Therefore, the piecewise function is: Obtaining Equations from Piecewise Function Graphs You may be asked to write a piecewise function, given a graph.

Put in numbers and try it! This means we can write this absolute value function as a piecewise function.

The purpose of this work is for students to think about the meaning of absolute value and how the absolute value function appears on a graph. I am particularly interested in whether students are more engaged in Problem 2 or Problem 3. Graphing Absolute Value Functions Example.

You might want to review Solving Absolute Value Equations and Inequalities before continuing on to this topic.Piecewise Functions A Function Can be in Pieces. We can create functions that behave differently based on the input (x) value.

A function made up of 3 pieces. Learn how to solve absolute value equations and how to graph absolute value functions. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance.

Absolute Value as a Piecewise Function We can write absolute value functions as piecewise functions – it’s really cool! You might want to review Solving Absolute Value Equations and Inequalities before continuing on to this topic.

Absolute Value Piecewise Functions Hit the "play" button on the player below to start the audio. You can use the forward and back buttons to navigate between the lesson's pages.

The only places where we need to break the function into "pieces" are those points where the expression inside each absolute value becomes zero. For students who don’t need to practice graphing the functions, they can start formulating a generalization about how to write a piecewise function directly from an absolute value function (see Absolute Value Piecewise Function Generalization).

Writing absolute value functions as piecewise equations
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