Question

Consider this absolute value function./(I) = |= + 31How can function fbe rewritten as a piecewise function?

Answer 1

Solution

We will look at the definition of absolute value function. See attached image below

Given

$f(x)=\lvert{x+3}\rvert$

Condition 1

$\begin{gathered} x+3\ge0 \\ x\ge-3 \end{gathered}$

Condition two

$\begin{gathered} x+3<0 \\ x<-3 \end{gathered}$

Definition 1 : The absolute value of (x + 3 ) is still ( x+ 3 )

Definition 2: The absolute value of ( x + 3) is negative ( x + 3 )

Finally , we will attach definition 1 and condition 1 and also definition 2 and condition 2 to obtain the piecewise function.

Final answer will be shown in the image below