Jo Steig The absolute value symbol is really shorthand for what we call a piecewise described function.
Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. Absolute Value Equations In the final two sections of this chapter we want to discuss solving equations and inequalities that contain absolute values.
Before solving however, we should first have a brief discussion of just what absolute value is. There are two ways to define absolute value. There is a geometric definition and a mathematical definition.
We will look at both. Also, we will always use a positive value for distance. Consider the following number line.
From this we can get the following values of absolute value. One way to think of absolute value is that it takes a number and makes it positive. We do need to be careful however to not misuse either of these definitions.
There is also the fact however that the right number is negative and we will never get a negative value out of an absolute value!
Well there are only two numbers that have a distance of 4 from the origin, namely 4 and So, this leads to the following general formula for equations involving absolute value. Example 1 Solve each of the following. Example 2 Solve each of the following. This is saying that the quantity in the absolute value bars has a distance of zero from the origin.
There is only one number that has the property and that is zero itself. That is exactly what this equation is saying however.
Likewise, there is no reason to think that we can only have one absolute value in the problem. So, we need to take a look at a couple of these kinds of equations.Some of the worksheets displayed are Piecewise functions date period, Work piecewise functions, Work piecewise functions, Piecewise functions, Writing equations for piecewise functions and word problems 2, Mathematics ii unit 5 step and piecewise functions part 1, Mat section work on piecewise functions, Absolute value and piecewise functions.
Absolute Value and Piecewise Functions Worksheet An Image/Link below is provided (as is) to download presentation complex numbers quadratic functions and equations inequalities rational equations radical equations absolute value equations.
willa cather –u.s. to write better code: more correct, easier to read/write/change. functions. Lesson – Graphing Absolute Value Functions Objectives: In this activity, students will relate the piecewise function to the graph of the absolute value function and continue their development of translating functions based on constants.
Synthesis Write an . A summary of Solving Equations Containing Absolute Value in 's Absolute Value. Learn exactly what happened in this chapter, scene, or section of Absolute Value and what it means.
Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans. If the expression inside the absolute value includes a variable, there is not much we can do with it as long as the absolute values are there.
Therefore, to get any work done we must first write it without absolute . Follow these steps to solve an absolute value equality which contains two absolute values (one on each side of the equation): Write two equations without absolute values.
The first equation will set the quantity inside the bars on the left side equal to the quantity inside the bars on the right side.