Answer:
[tex]f(x)=\left\{\begin{array}{l}x+3,\ \ x< 0\\ \\3,\ \ x\ge 0\end{array}\right.[/tex]
Step-by-step explanation:
The graph of a function is shown in attached diagram.
1. Write the equation of the left part. This is the straight line with the slope of
[tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-3}{-5-0}=\dfrac{-5}{-5}=1[/tex]
So, the equation of the line is
[tex]y=1\cdot x+b\\ \\y=x+b,[/tex]
where b is the y-intercept.
This graph intersects the y-axis at point (0,3), so b = 3.
Therefore,
[tex]y=x+3[/tex]
2. The equation of the right part is y = 3.
3. The expression for the function represented by the graph is
[tex]f(x)=\left\{\begin{array}{l}x+3,\ \ x< 0\\ \\3,\ \ x\ge 0\end{array}\right.[/tex]
