SOLUTION: Determine whether the graph of y = | x | + 3 is symmetric with respect to the origin, the x-axis, or the y-axis.

Question 466479: Determine whether the graph of y = | x | + 3 is symmetric with respect to the origin, the x-axis, or the y-axis.
Answer by ccs2011(207) (Show Source): You can put this solution on YOUR website!
Graph of

To test for symmetry, imagine folding the graph along an axis
If the graph folds on top of each other it is symmetric
Thus it is symmetric about the y-axis
Another way to check is to use points:
If its symmetric about the y-axis then:
For all points (a,b) if point (a,b) is on graph then point(-a,b) will also be on graph
Let (a,b) be (2,5) --> y = |2| +3 = 5
Then evaluate (-2,5) --> y = |-2| +3 = 2+3 = 5
It works
If its symmetric about the x-axis then:
For all points (a,b)if point (a,b) is on graph then point(a,-b) will also be on graph
Let (a,b) be (2,5) --> y = |2| +3 = 5
Then evaluate (2,-5) --> y = |2| +3 = 5
It Does Not work
If its symmetric about the origin then:
For all points (a,b)if point (a,b) is on graph then point(-a,-b) will also be on graph
Let (a,b) be (2,5) --> y = |2| +3 = 5
Then evaluate (-2,-5) --> y = |-2| +3 = 2+3 = 5
It Does Not work
Therefore the function is only symmetric about y-axis
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