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Question 1123437: y=|x-1|-2 graph each equation. thanks!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
The idea is to plug in various values of x to determine the corresponding y output value
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Plug in x = -1 and then use the order of operations PEMDAS to simplify
y = |x-1|-2
y = |-1-1|-2 ..... every x has been replaced with -1
y = |-2|-2
y = 2-2
y = 0
So when x = -1, the y value is y = 0. This means the point (x,y) = (-1,0) is on the graph.
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Plug in x = 0
y = |x-1|-2
y = |0-1|-2 ..... every x has been replaced with 0
y = |-1|-2
y = 1-2
y = -1
The point (0,-1) is another point on this graph.
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Plug in x = 1
y = |x-1|-2
y = |1-1|-2 ..... every x has been replaced with 1
y = |0|-2
y = 0-2
y = -2
The point (1,-2) is another point on the graph
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The process shown above is repeated as many times as you want to generate any number of points. The process can go on infinitely. The more points you generate, the more accurate the graph will be.
Here is a table that shows the various points when x ranges from -5 to 5. The value of x only takes on integer values (positive or negative whole numbers).
| x | y |
|---|
| -5 | 4 | | -4 | 3 | | -3 | 2 | | -2 | 1 | | -1 | 0 | | 0 | -1 | | 1 | -2 | | 2 | -1 | | 3 | 0 | | 4 | 1 | | 5 | 2 |
Once you know what points you'll use, plot them all on the same xy coordinate grid system (aka graph paper). This is what that looks like for the points shown above in the table
The last step is to draw a line or curve through all of the points. This is what the graph would look like (the blue points can be optionally taken out after you graph the red lines)
What we get is a V shaped graph that has the loweset point (known as the vertex) to be located at the point (1,-2)
To get this graph using transformations of the parent function y = |x|, we shift 1 unit to the right and 2 units down. Note how the origin point (0,0) moves along this path.
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