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Describing Transformations of Absolute Value Functions

Describing Transformations of Absolute Value Functions 1.13 - Solution

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

Graphing g(x)g(x)

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

xx 2x2\left|x\right| Simplify g(x)g(x)
-3{\color{#0000FF}{\text{-}3}} 2-32\left|{\color{#0000FF}{\text{-}3}}\right| 2(3)2(3) 66
-2{\color{#0000FF}{\text{-}2}} 2-22\left|{\color{#0000FF}{\text{-}2}}\right| 2(2)2(2) 44
-1{\color{#0000FF}{\text{-}1}} 2-12\left|{\color{#0000FF}{\text{-}1}}\right| 2(1)2(1) 22
0{\color{#0000FF}{0}} 202\left|{\color{#0000FF}{0}}\right| 2(0)2(0) 00
1{\color{#0000FF}{1}} 212\left|{\color{#0000FF}{1}}\right| 2(1)2(1) 22
2{\color{#0000FF}{2}} 222\left|{\color{#0000FF}{2}}\right| 2(2)2(2) 44
3{\color{#0000FF}{3}} 232\left|{\color{#0000FF}{3}}\right| 2(3)2(3) 66

Now we can plot these ordered pairs on a coordinate plane and connect them to get the graph of g(x).g(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 stretch of the graph f(x)f(x) by a factor of 2.2.