Question 147034
Absolute value equations such as this one are shaped like the letter "V"
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An easy way to graph this one is to assign some positive and negative values to x, then determine
the corresponding value of y for each value of x, and finally plot the points and sketch in the
graph.
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Suppose we let x = 0. Then the equation becomes:
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{{{y = abs(0 - 2) - 2 = abs(-2) - 2 = 2 - 2 = 0}}}
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So one point on the graph is (0, 0)
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Suppose we let x = -4. Then the equation becomes:
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{{{y = abs(-4 - 2) - 2 = abs(-6) - 2 = 6 - 2 = 4}}}
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So another point on the graph is (-4, 4)
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Suppose we let x = -2. Then the equation becomes:
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{{{y = abs(-2 - 2) - 2 = abs(-4) - 2 = 4 - 2 = 2}}}
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So another point on the graph is (-2, 2)
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Suppose we let x = +2. Then the equation becomes:
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{{{y = abs(2 - 2) - 2 = abs(0) - 2 = 0 - 2 = -2}}}
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So another point on the graph is (2, -2)
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Suppose we let x = +4. Then the equation becomes:
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{{{y = abs(4 - 2) - 2 = abs(2) - 2 = 2 - 2 = 0}}}
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So another point on the graph is (+4, 0)
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Finally, suppose we let x = +5. Then the equation becomes:
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{{{y = abs(5 - 2) - 2 = abs(3) - 2 = 3 - 2 = 1}}}
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So another point on the graph is (+5,+1)
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And you can continue this process of assigning values to x and determining the corresponding
values of y until you have enough coordinate pairs to determine what the graph looks like.
When you get done plotting those points for this problem, your graph should look like:
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{{{graph(300,300,-6,+6,-6,+6,abs(x-2)-2)}}}
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Hope this helps you to see one way of doing this graphing problem.
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