Graphs of Absolute Value Equations

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Graphing Composite Absolute Value Functions

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Key Questions

  • Let's start with a simple one #y=|x+2|#

    If #x> -2#, #x+2# is positive, so #y=|x+2|=x+2#
    If #x<-2#, #x+2# is negative, but will be 'turned around' by the abslote signs, so in this domain #y=|x+2|=-x-2#

    These two semi-graphs meet at #(-2,0)#
    graph{|x+2| [-10.5, 9.5, -1.08, 8.915]}

  • The shape of a graph with an absolute value would look something similar to a "V".

    graph{abs(x) [-10, 10, -5, 5]}

    This graph has a slope of #1# on the right of the #y#=axis and #-1# on the left of the #y#-axis

  • #y = a abs(x-h)+k# has vertex #(h, k)#

    #y = 3 abs(x-1)+5# has vertex #(1, 5)#

  • A table of values is simply a pairing between an input and an output. Absolute value equations can range from very complex to relatively simple -- there are also many theorems and postulates that dictate the behavior of absolute value equations in various circumstances.

    In its purest form, absolute value makes all numbers positive. For instance, # y = |x| # would result in the positive form of #x# being the output, whether #x# is positive or negative. For instance, if #x# is #-5#, it would be #5# when it comes out of that equation. Create a table of values like you normally would, but compute values enclosed in absolute value markers as positive.

    Another common form of absolute value equations can be found in a form similar to #|a-3| = 5#

    Thus:

    #|a-3| = 5# would have #a# values # -2 < x < 8 #

    From there, you can create a table from the values of #a#.

    If you can update your question with more detail, I may be able to answer it better.

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