How do you graph #y=-abs(x-8)+1#?

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Answer 1 · 2017-11-29T01:03:32

See below

#y=-abs(x-8)+1#

When approaching a graphing problem of this nature it may be easier to consider the following steps.

Step 1. The graph of #abs(x-8)# is the 'V-graph' formed as follows:

#f(x) = -(x-8)# for #x in (-oo, 8)#
#f(8) = 0#
#f(x) =+(x-8) # for #x in (8, +oo)#

Step 2. The graph of #-abs(x-8)# is the mirror reflection of the graph in Step 1 about the #x-#axis

Step 3. The graph of #-abs(x-8)+1# is the graph from Step 2 transformed ("shifted") 1 unit positive ("up") on the #y-#axis.

The resultant graph of #y# is shown below.

graph{-abs(x-8)+1 [-0.65, 11.84, -3.324, 2.92]}