Linear Absolute Value Function

linear absolute value equations based on real-world situations. Students begin with a graphical representation of a linear absolute value function and use a horizontal line to solve an equation. With a solid visual understanding of the structure of a linear absolute value function, students then solve these equations.

One of the functions that falls under the category of a piecewise-defined function is the Absolute Value Function. we have seen, by its definition, that the function is actually composed of two linear quotpiecesquot. When graphing functions, remember that y f x, allowing for either quotyquot or quotf xquot to represent the function.

Graphs of Absolute Value Functions and their Symmetry . Write as a piecewise-defined linear function. In Exercises 13 - 18, graph the function by rewriting each function as a piecewise defined function using Definition 1.12. Find the axis intercepts of each graph, if any exist. From the graph, determine the domain and range of each

So far in this chapter we have been studying the behavior of linear functions. The Absolute Value Function is a piecewise-defined function made up of two linear functions. The name, Absolute Value Function, should be familiar to you from Section 1.2. In its basic form92fx92leftx92right92 it is one of our toolkit functions.

1.2 Transformations of Linear and Absolute Value Functions 13 EXAMPLE 2 Writing Refl ections of Functions Let fx x 3 1. a. Write a function g whose graph is a refl ection in the x-axis of the graph of .f b. Write a function h whose graph is a refl ection in the y-axis of the graph of f. SOLUTION a. A refl ection in the x-axis changes the sign of each output value.

Linear Functions. Represent a linear function with an equation, words, a table and a graph Determine whether a linear function is increasing, decreasing, or constant Write and interpret a linear function Graphs of Linear Functions. Graph linear functions by plotting points, using the slope and y-intercept, and by using transformations

The function inside the absolute value, 2x1, is linear, so the graph is composed of straight lines. The graph of y 2 x 2 1 is curved, and it does not have a single vertex, but two quotcusps.quot The function inside the absolute value is NOT linear, therefore the graph contains curves. Example 4. Sketch a graph of the function. f x

Linear and Absolute Value Function Families. In this Concept we will examine several families of functions. A family of functions is a set of functions whose equations have a similar form. The parent of the family is the equation in the family with the simplest form. For example, y x 2 is a parent to other functions, such as y 2x 2 - 5x 3.

Absolute value is a mathematical function that takes the positive version of whatever number is inside the absolute value signs, which are drawn as two vertical bars. For example, the absolute value of -2 -- written as -2 -- is equal to 2. In contrast, linear equations describe the relationship between two variables. For example, y 2x 1 tells you that to calculate y for any given value of

I would simply define a linear function as always having the same slope and, more technically, it must be continuous. Clearly, the absolute value function has a negative slope for values lt 0 and positive slope for values gt 0. So it's not linear.