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Chapter 3: Problem 88

Begin by graphing \(y=|x| .\) Then use this graph to obtain the graph of \(y=|x-2|+1 . \quad \text { (Section } 1.6, \text { Example } 3)\)

Short Answer

Expert verified
The graph of \(y = |x|\) is a V-shaped graph intersecting the origin. The graph of \(y = |x - 2|\) is the same V-shaped graph shifted 2 units to the right. The graph of \(y = |x - 2| + 1\) is the graph of \(y = |x - 2|\) shifted up by 1 unit.

Step by step solution

01

Graph \(y = |x|\)

First, graph the parent function \(y = |x|\). The graph would intersect at the origin (0,0) and rise at a 45 degree angle to the right of the y-axis and left of the y-axis, forming a 'V' shape.
02

Graph \(y = |x - 2|\)

Now, to get the graph of \(y = |x - 2|\), take the graph of \(y = |x|\) and shift every point 2 units to the right since subtracting a positive number from x in the absolute value results in moving the graph to the right. This is the result of the operation inside the absolute value.
03

Graph \(y = |x - 2| + 1\)

Finally, to get the graph of \(y = |x - 2| + 1\), take the graph of \(y = |x - 2|\) and shift every point 1 unit up, since adding a positive number outside the absolute value takes every value of y in the graph upwards. This is the result of the operation outside the absolute value.

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