Question

unit test
unit test complete
11 12 13 14 15
the graph of a function is shown. which function is represented by the graph?
options:
$f(x)=\

$$\begin{cases}x - 3, & x < 0 \\\\ 3, & x \\geq 0\\end{cases}$$

$
$f(x)=\

$$\begin{cases}x + 3, & x < 0 \\\\ 3, & x \\geq 0\\end{cases}$$

$
$f(x)=\

$$\begin{cases}-x + 3, & x \\leq 0 \\\\ 3, & x > 0\\end{cases}$$

$
$f(x)=\

$$\begin{cases}-x - 3, & x \\leq 0 \\\\ 3, & x > 0\\end{cases}$$

$
mark this and return save and exit next subm

Explanation:

Step1: Analyze $x>0$ part

The graph is horizontal at $y=3$ for $x>0$, so the second piece is $3$.

Step2: Analyze $x\leq0$ part

The line for $x\leq0$ passes through $(0,3)$ and $(-3,6)$. Slope $m=\frac{6-3}{-3-0}=-1$. Using point-slope form $y - 3=-1(x - 0)$, so $y=-x + 3$.

Step3: Match the function

Combine both pieces: $f(x)=

$$\begin{cases}-x + 3, & x\leq0 \\3, & x>0\end{cases}$$

$, which is option C.

Answer:

C. $f(x)=

$$\begin{cases}-x + 3, & x\leq0 \\3, & x>0\end{cases}$$

$