Answered

The graph of a function is shown.
2-
54-3-2-1 12345x
2
23
4-
Which function is represented by the graph?
Of(x)=
x-3, x<0
3,
O f(x)=
x+3, x<0
3,
-x+3, x ≤0
Of(x)=
3,
x>0
○ f(x)=
-x-3, x ≤0
3,

Verified Answer :

yuzhong885

Answer:

\[ f(x) = \begin{cases}

x + 3 & \text{if } x < 0 \\

3 & \text{if } x \geq 0

\end{cases} \]

Step-by-step explanation:

To determine the function represented by the graph, we need to analyze the graph's behavior in different regions. From what you've shown, it appears that the function is defined differently for \( x < 0 \) and \( x \geq 0 \).

For \( x < 0 \), the graph appears to be a line starting at (0, 3) with a slope of 1, which corresponds to the function \( f(x) = x + 3 \).

For \( x \geq 0 \), the graph is a horizontal line at y = 3, which corresponds to the function \( f(x) = 3 \).

So, combining both cases, the function represented by the graph is:

\[ f(x) = \begin{cases}

x + 3 & \text{if } x < 0 \\

3 & \text{if } x \geq 0

\end{cases} \]

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