Question

unit test
unit test complete
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the graph of a function is shown.
which function is represented by the graph?
(graph: a coordinate plane with a line from (-5, -2) passing through (-3, 0) to (0, 3), then a horizontal line from (0, 3) to the right. the y-axis is labeled from -5 to 5, x-axis from -5 to 5.)
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 s

Explanation:

Step1: Analyze the right part ($x\geq0$)

The graph is a horizontal line at $y=3$ for $x\geq0$, so the function here is $f(x)=3$.

Step2: Analyze the left part ($x<0$)

The line for $x<0$ has a slope of 1 (rises 1 unit for each 1 unit right) and y-intercept at $(0,3)$. Using $y=mx+b$, it is $y=x+3$.

Step3: Match with options

The piecewise function is

$$\begin{cases} x+3, & x<0 \\ 3, & x\geq0 \end{cases}$$

, which is option B.

Answer:

B. $f(x)=

$$\begin{cases} x+3, & x<0 \\ 3, & x\geq0 \end{cases}$$

$