Piecewise-Defined Functions

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Question

Piecewise-Defined Functions

Find a formula for each function graphed in Exercises 29–32.

b.

Accepted Answer

Welcome back, everyone. In this problem, determine the PA formula of the given function as shown. Now, if we take this function here, OK, notice that this function is made up of three horizontal lines. So, if we're going to determine the piece as formula, first, we need to find the equations of each piece of our function and then specify what those equations would be for which given intervals. OK? So, no, because these are horizontal lines, recall that generally, OK, a horizontal line. Is an equation, OK, is an equation. In the farm Y equals k where k is some constant, and that's because the slope here is 0 and it indicates that every point on each line has the same Y coordinate. OK, so no, because of that, each of our lines will have a separate equation depending on the interval. So for example, let's take the blue segment. Here, notice that the Y values are always 2, so therefore each equation is Y equals 2. For the red or orange segment here, all of its Y coordinates are 3, so its equation is Y equals 3. While for the green segment, its equation is Y equals 1. Know that we have the equations, all we need to do is to put their intervals. OK? In other words, if we were to think about our formula, now we know that Y equals. 23, and 1. But now, let's specify on what intervals, OK? Let me make some space here actually. So 23 and 1. I think I'll have to just get rid of these as well and rewrite it. But now, let's specify the intervals. OK. Now, for equation Y equals 2. Not that it's closed at 0 and open at 1. So its interval is 0 less than or equal to x 1. In other words, X is greater than or equal to 0 but less than 1. For Y E equals 3, notice that it's closed at 1 and open at 2. So its domain or its interval is 1 less than or equals X 2. Finally, when Y E equals 1, the domain is closed at 2 and open at 3. So its domain is 2 less than or equal to X, less than 3, OK? Thus, this is the piece wise formula of our function. Thanks a lot for watching everyone. I hope this video helped.

Piecewise-Defined Functions

Find a formula for each function graphed in Exercises 29–32.

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Key Concepts

Piecewise Functions

Domain and Range

Graph Interpretation

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