Question 466479
Graph of {{{y = abs(x) + 3}}}
{{{graph(200,200,-4,4,-1,7,abs(x) + 3)}}}

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