![]() ![]() There are two criteria for naming piecewise functions: The format for defining piecewise functions has this general form: This function is made up of pieces of parallel linear functions that are one unit long This function is also called the castle rim function. Next, we have the sawtooth function, f of x equals x minus the floor of x. This function is made up of pieces of constant functions that are 1 unit wide. This is also called the floor function or stair step function. Let’s take a quick break and practice describing a couple of piecewise functions in terms of what their pieces look like and where those pieces are defined.įirst up is the greatest integer function, f of x equals the floor of x. One way to visualize this is to graph both linear functions and erase the sections that are not part of the absolute value function. If the left function is only defined for negative x-values and the right is only defined for positive x-values (and we put the 0 into one of them – more on that in a minute), we can define this as a single piecewise function. So each piece needs to be defined on a section of its domain in order to define a piecewise function. Normally, both f of x equals negative x and f of x equals x also have domains of all real numbers, but if we were to graph them together, the graph would look like this and we would no longer have a function. The domain of the absolute value function is all real numbers. At that point, the function definition changes to f of x equals x. On the left, f of x equals negative x and on the right, f of x equals x.Īs we “read” the graph from left to right, we are on the function f of x equals negative x until x=0. Instead of a single V, f(x) can also be visualized as pieces of two linear functions. This is the graph and a section of the table of values of f of x equals the absolute value of x : Functions in the absolute value family have equations that resemble f of x equals the absolute value of x and their graphs all have a characteristic “V” shape. The first piece we’re going to look at is the absolute value function. As the name suggests, they are functions comprised of pieces of other functions. Piecewise functions are not considered a function family on their own. Functions in the quadratic family have equations that look like f of x equals a x squared and their graphs are parabolas. Many functions belong to function families because their equations and graphs all have similar characteristics.įor example, functions in the linear family have equations that resemble f of x equals mx plus b and their graphs are straight lines. A function is a relationship where a single output is assigned to each input. And how piecewise functions can be usedįirst, let’s look at the definition of a function.Hi, and welcome to this video about piecewise functions! In this video, we will explore ![]()
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