# How to write absolute value equations as piecewise equations and inequalities

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. When they make this connection, they will be able to reason about and visualize absolute value functions more efficiently MP7.

We learned how about Parent Functions and their Transformations here in the Parent Graphs and Transformations section. The questions also show different transformations of the function.

You might want to review Quadratic Inequalities for the second example below: Put in numbers and try it! A dialogue might proceed as follows: Look for and make use of structure. I am particularly interested in whether students are more engaged in Problem 2 or Problem 3.

Welcome to She Loves Math! 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.

Learn these rules, and practice, practice, practice! You may also be asked to take an absolute value graph and write it as a piecewise function: So, the piecewise function is: 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.

Therefore, the piecewise function is: Here are the graphs, with explanations on how to derive their piecewise equations: We have to start at 0, since dogs have to weigh over 0 pounds: The piecewise function is: What is another option?

This means we can write this absolute value function as a piecewise function. Here are more examples, with explanations.There are many opportunities for mistakes with absolute-value inequalities, so let's cover this topic slowly and look at some helpful pictures along the way.

the solution is TWO inequalities, not one. DO NOT try to write this as one inequality. If you try to write this solution as "–2 College Math. College Pre-Algebra Introductory. An absolute value equation is an equation that contains an absolute value expression.

The equation You can write an absolute value inequality as a compound inequality. \left | x \right |absolute value equations and inequalities; Linear inequalities in two variables. 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. and click on Write the Absolute Value as Piecewise. "Undo" the absolute value signs by making the expressions inside the absolute value sign negative or positive.

Take all the inequalities obtained (these are all solution sets) and figure out the solution set. Algebra Examples. Step-by-Step Examples.

Algebra. Absolute Value Expressions and Equations. Write the Absolute Value as Piecewise. The piecewise polynomials are when and when. Remove parentheses. Solve for when.

ABSOLUTE VALUE AND PIECEWISE FUNCTIONS In order to remove the absolute value sign from a function you must: 3. Rewrite the equation without the absolute value as a piecewise function.

For each interval where the expression is positive we can write that interval by just dropping the absolute value. Write as a piecewise .

How to write absolute value equations as piecewise equations and inequalities
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