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Describing Transformations of Absolute Value Functions

Describing Transformations of Absolute Value Functions 1.6 - Solution

arrow_back Return to Describing Transformations of Absolute Value Functions

Let's graph g(x)g(x) first and then we can compare it to the graph of the parent function.

Graphing g(x)g(x)

To graph the function, let's make a table of values first.

xx x5.5\left|x\right|-5.5 Simplify g(x)g(x)
-5{\color{#0000FF}{\text{-}5}} -55.5\left|{\color{#0000FF}{\text{-}5}}\right|-5.5 55.55-5.5 -0.5\text{-}0.5
-3{\color{#0000FF}{\text{-}3}} -35.5\left|{\color{#0000FF}{\text{-}3}}\right|-5.5 35.53-5.5 -2.5\text{-}2.5
-1{\color{#0000FF}{\text{-}1}} -15.5\left|{\color{#0000FF}{\text{-}1}}\right|-5.5 15.51-5.5 -4.5\text{-}4.5
0{\color{#0000FF}{0}} 05.5\left|{\color{#0000FF}{0}}\right|-5.5 05.50-5.5 -5.5\text{-}5.5
1{\color{#0000FF}{1}} 15.5\left|{\color{#0000FF}{1}}\right|-5.5 15.51-5.5 -4.5\text{-}4.5
3{\color{#0000FF}{3}} 35.5\left|{\color{#0000FF}{3}}\right|-5.5 35.53-5.5 -2.5\text{-}2.5
5{\color{#0000FF}{5}} 55.5\left|{\color{#0000FF}{5}}\right|-5.5 55.55-5.5 -0.5\text{-}0.5

Now we can plot these ordered pairs on a coordinate plane and connect them to get the graph of the parent function, f(x)=x.f(x)=|x|. Notice that g(x)g(x) is a transformation of f(x)f(x) and the graph of f(x)=xf(x)=|x| is V-shaped. Thus, g(x)g(x) will also be a V-shaped graph.

Comparing the Functions

To compare our graph to the graph f(x)=x,f(x)=|x|, let's draw them on one coordinate plane.

As we can see, the graph of g(x)g(x) is a vertical translation 5.55.5 units down of the graph f(x).f(x).