How do you graph #y=abs(x)-2#?

1 Answer
John D.
Jul 20, 2017

The graph looks like this:

graph{y=absx-2 [-10.125, 9.875, -5, 5]}

Explanation:

The absolute value function #y=absx# looks like this:

graph{y=absx [-9.875, 10.125, -3.68, 6.32]}

This is a function you should probably know well for the future. Anyway, in order to plot #y = absx - 2#, we need to shift the #y# values down by #2#, since we are subtracting two from what #y# is.

I would start graphing this graph by plotting the vertex (the point where the graph has a tight corner). On the original graph it is #(0,0)#, so on the new graph it will be #(0,-2)#.

graph{x^2+(y+2)^2<=.04 [-9.875, 10.125, -3.68, 6.32]}

Now you need to draw the two rays coming from this point. To do this, graph one point on either side of #(0,2)# and connect it to #(0,2)#. Let's use #x=-2# and #x=2#.

#y = abs(-2)-2 = 2 - 2 = 0#

#y= abs2-2 = 2-2 = 0#

So now we know the points #(-2,0)# and #(2,0)# are on our graph.

graph{(x^2+(y+2)^2-0.04)((x-2)^2+y^2-0.04)((x+2)^2+y^2-0.04) = 0 [-10.125, 9.875, -5, 5]}

Now all that you have to do is connect these points.

graph{y=absx-2 [-10.125, 9.875, -5, 5]}

Final Answer

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