Active participation through direct questioning 6. Research Students should research real-world applications of piecewise functions. Write the word problem real-world application. Write the piecewise function for the word problem.

Now, let's graph this function using the points the chart above to plot our coordinates: Graph of the absolute value function: Notice, also that the domain is because we can substitute anything real number in for x.

Our range runs from because we have no negative outputs for the function.

A Real-Life Application Why study piecewise functions? Well, there are some real-life practical examples for studying piecewise linear functions. For example, we can talk about "flat" income tax versus a "graduated" income tax. A flat income tax would tax people at the same rate regardless of their income.

Some people think that flat tax is unfair for those in or near the poverty level because they are getting taxed at the same rate as those in a higher income bracket. Our income tax is based on a graduated tax calculation. This would be an example of a piecewise continuos linear function.

Let's take a look at the two graphs and discuss them. Graph of flat versus graduated taxes Note that the flat tax rate has a constant slope of.

Either equation above will work, the second one is just a simplified version of the first. Now, in the last piece of the graduated tax, the income from [45, to "infinity"] is calculated as follows: These are both explained above.

So, we have a 3-piece equation for our graduated taxes as follows: From the graph above, we see that the flat tax is worse for people in the lower income, as the flat tax line is above the graduated tax line.

However, note the characteristic of the graphs as income increases. For which incomes s would the flat tax and the graduated tax be the same? We will discuss how to arrive at the algebraically in the next section, "Linear Systems. Note that these percentages are fictitious, so if you are planning to make a real-life decision, make sure you know the correct tax percentages!Piecewise Functions Create a table for each graph.

Then describe the graph in words. 1. a. Use the endpoints and points close to them as the domain values in the table. Evaluate each piecewise function for x 3 and x 4.

3. f x { 10 if x 4 1 if x 4 4. g 2 x { 3x if 1 . Worksheet Piecewise Functions Name: Part attheheels.comlly graph each of the following. Identify whether or not he graph is a function. Then, evaluate the graph at any specified domain value.

Unit 1 Guided Notes Functions, Equations, and Graphs Standards: ⃣Compare properties of two functions each represented in different ways Linear Functions in Writing a Piecewise Function Example 2: Write the equation for the piecewise function below Steps: 1. Find your intervals. The following graph is called a piecewise function because the function is defined by two or more different equations applied to different parts of the function’s domain.

Notice that it appears to be composed of three segments, each a. Continuity of piecewise functions. Here we use limits to check whether piecewise functions are continuous.

The Intermediate Value Theorem Two young mathematicians look at graph of a function, its first derivative, and its second derivative.

Set and write. A step function is a piecewise function defi ned by a constant value over each part of its domain. The graph of a step function consists of a series of line segments.

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Eleventh grade Lesson Graphing and Writing Equations for Piecewise Functions