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Analyzing Graphs of Absolute Value Functions

Analyzing Graphs of Absolute Value Functions 1.6 - Solution

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We are asked to draw the graph of f(x)=-x+32.f(x)=\text{-} |x+3|-2. To do so, we will use a table of values to find points on the graph. Recall that the absolute value removes the negative sign. In this case, however, we have a negative sign preceding the absolute value. This will take each positive value created by the absolute value and then make it negative, regardless of its original sign.

xx -x+32\text{-} |x+3|-2 Simplify absolute value f(x)=-x+32f(x)=\text{-} |x+3|-2
-7{\color{#0000FF}{\text{-} 7}} --7+32\text{-} |{\color{#0000FF}{\text{-} 7}}+3|-2 -(4)2\text{-} (4)-2 -6\text{-} 6
-5{\color{#0000FF}{\text{-} 5}} --5+32\text{-} |{\color{#0000FF}{\text{-} 5}}+3|-2 -(2)2\text{-} (2)-2 -4\text{-} 4
-3{\color{#0000FF}{\text{-} 3}} --3+32\text{-} |{\color{#0000FF}{\text{-} 3}}+3|-2 -(0)2\text{-}(0)-2 -2\text{-} 2
-1{\color{#0000FF}{\text{-}1}} --1+32\text{-} |{\color{#0000FF}{\text{-}1}}+3|-2 -(2)2\text{-}(2)-2 -4\text{-} 4
1{\color{#0000FF}{1}} -1+32\text{-} |{\color{#0000FF}{1}}+3|-2 -(4)2\text{-}(4)-2 -6\text{-} 6

Now, we will plot and connect the obtained points. Doing that we keep in mind that the graph of an absolute value function has a V shape.