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How do you graph a piecewise function? Given a graph, how do you write an equation for a piecewise function? Give examples for each.

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02:46

How do you graph a piecewise function?

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The graph of a piecewise-defined function is given. Write a definition for each function.

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Transcript

All right taking a peek at piece, wise functions, there’s a couple of ways to graph. You can graph the linear functions for the entire domain and then erased the portion. You don’t want. Otherwise what you can do is determine where the end point is going to be. So what were gonna do is we’re gonna. Take this first linear equation: negative 1, half x plus 4. The domain restriction for that portion of our piece wise function is x is less than negative. 4, since x is less than negative 4. We know there’s going to be an open circle, so what i do is i plug in negative 4 to x, so we have negative 1 half times. Negative 4 is 22 plus 4 is 6, so at negative 46. We do have this open circle all right and from that point we have a slope of negative 1 half, which means i normally would go down 1 and over 2. However, our restriction indicates we go to left so we’re going to go up 1 and left 2 to plot that line. The second part of our piece wise function is just the line essentially y equals 2. It’S a horizontal line from negative 4 to 2 point we’re going to have a closed circle at negative 4 and an open circle at 2. So at negative 42 were closed. Circle 22, we’re going to have an open circle, and then we just connect those to create our line for that part of our piece wise graph. Finally, the third example in this case we have 3 x minus 4 point. So again, just like before i’m gonna take this 2, i’m gonna plug it in 3 times 2 is 66. Minus 4 is 2, so at 2 to we actuall have a closed circle. Whenever you have a closed circle in an open circle. On the same point, it’s going to appear closed,…

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