Answers: Check out the attached image to see how the boxes are filled out
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Step-by-step explanation:
This piecewise function is considered a step function or a staircase function, because the graph is somewhat similar to such real life structures (though the vertical portions are not present; or else we wouldn't have a function).
Notice that your teacher has already filled in "1" for you. This is due to the horizontal portion on the very left side of the graph that has a height of 1. In other words, every point on this horizontal line has y coordinate y = 1. This horizontal line only applies when -3 <= x < -1
The notation -3 <= x is the same as saying
, but I'll stick with the first format.
So in short, we'll write -3 <= x < -1 in the box of the first row. This tells us how much of the y = 1 line to draw.
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The second row will have the same idea as the first row. We first state what we want to graph, then we state what are the x input boundaries (so we don't graph that piece forever).
The second piece is y = 2 due to this height value. We simply put "2" without quotes into the first box of row 2. It's a coincidence that the row number and what we're inputting here are the same.
This center piece only is drawn when -1 <= x < 1 since we have a closed circle at x = -1, but an open circle at x = 1.
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The third row is a repeat of ideas of the previous two rows. This time the height is y = 3 and this horizontal portion is only graphed when 1 <= x < 3.
Refer to the image below to see where all of the pieces go.