Consider this absolute value function.f(x) = |x-5|how can the function f be written as a piecewise function

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asked Jul 13, 2023 76.4k views

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Chester Husk · Answer 1 · 2023-07-19T17:23:32+0000

Solution

By definition

$|y|=\begin{cases}y,\text{ }y\ge0 \\ {} \\ {-y,\text{ }y<0}\end{cases}$

Graphically, what |y| represents is

If y = x -5

$\begin{gathered} \Rightarrow f(x)=|x-5|=\begin{cases}{x-5\text{ if }x-5\ge0} \\ {} \\ {-(x-5)\text{ if }x-5<0}\end{cases} \\ \\ \\ \operatorname{\Rightarrow}f(x)=\lvert x-5\rvert=\begin{cases}{x-5\text{ if }x\ge5} \\ {} \\ {-x+5\text{ if }x<5}\end{cases} \end{gathered}$

The correct option is D.

To have a better understanding of it lets graw its graph

consider this absolute value function.f(x) = |x-5|how can the function f be written-example-1

Consider this absolute value function.f(x) = |x-5|how can the function f be written as a piecewise function

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