Graph the function. $f ( x ) = - | x + 4 |$

Question

Quizplus · Accepted Answer

To graph the function, we can first examine the piecewise definition of absolute value:
$$|x| = \begin{cases} 
      x & x\geq 0 \
      -x & x<0 \
   \end{cases}
$$
Thus,
$$|x+4| = \begin{cases} 
      x+4 & x+4\geq 0 \
      -(x+4) & x+4<0 \
   \end{cases}
$$
Simplifying, we get
$$|x+4| = \begin{cases} 
      x+4 & x\geq -4 \
      -(x+4) & x< -4 \
   \end{cases}
$$
Then, for $f(x)=-|x+4|$, we can graph two parts separately. When $x\geq -4$, $|x+4|=x+4$, so $f(x)=-|x+4|=-x-4$. This represents a line with slope $-1$ and $y$-intercept $-4$. When $x<-4$, $|x+4| = -(x+4)$, so $f(x)=-|x+4|=x+4$. This also represents a line with slope $1$ and $y$-intercept $4$. Therefore, the graph looks like the following:

![Graph of f(x)=-|x+4|](https://i.imgur.com/qE5pFKY.png)

Option B is the correct graph.

Graph the Function f(x)=−∣x+4∣f ( x ) = - | x + 4 |f(x)=−∣x+4∣

Graph the Function $f ( x ) = - | x + 4 |$