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# Analyzing Graphs of Absolute Value Functions

## Analyzing Graphs of Absolute Value Functions 1.6 - Solution

We are asked to draw the graph of $f(x)=\text{-} |x+3|-2.$ 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.

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

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.