Linear Absolute Value Function Math Definition

Then the absolute value of 8 is 8 and we write 8 8. This function takes a value x and makes it positive. To graph an absolute value function choose several values of x and find some ordered pairs.

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So far in this chapter we have been studying the behavior of linear functions.

Linear absolute value function math definition. Home courses mathematics algebra ii. The first graph shows 6 located at a distance of 6 units from zero. Definition of absolute value. The second graph shows 8 located at a distance of 8 units from zero.

In its basic form f x x it is one of our toolkit functions. The absolute value of a number is the distance the number is from zero. The equation for an absolute value function has the general form. An absolutely integrable function also called a summable function has an integrable absolute value.

Y a x h k it would be rather scary if we just threw this equation at you with a bunch of letters sitting there without context. Interpret the equation y mx b as defining a linear function whose graph is a straight line. There are a few ways to describe what is meant by the absolute value x of a real number x. For instance f 4 4 4 f 7 7 7 and f 234 234 234.

For example the function a s sup 2 sup giving the area of a square as a function of its side length is not linear because its graph contains the points 1 1 2 4 and 3 9 which are not on a straight line. 24 2019 4 52 p m. Give examples of functions that are not linear. Linear and absolute value functions classwork homework.

You may have been taught that x is the distance from the real number x to 0 on the number line. The absolute value parent function written as f x x is defined as. The name absolute value function should be familiar to you from section 1 2. F x x if x 0 0 if x 0 x if x 0.

So for example 5 5 and 5 5 since each is 5 units from 0 on the number line. The absolute value function is given as f x x. The absolute value function is a piecewise defined function made up of two linear functions. Linear function review systems of linear equations.

Linear and absolute value functions extra practice. Recall that the absolute value of a number is its distance from 0 on the number line. Linear and absolute value functions unit. An absolute value function is a function that contains an algebraic expression within absolute value symbols.

Integrable means that you can find an integral. The absolutely portion of the term refers to the fact that it s the absolute value of the function that must be integrable on the real line feeman 2015.