Since we have a piecewise function containing three functions, then we will have three separate graphs here.
Let's start with the first function: f(x) = 3 when x ≤ -3.
Moving on to the next function: f(x) = 2x + 1 when -3 < x < 4.
Assume x = -3.
[tex]\begin{gathered} f(x)=2x+1 \\ f(-3)=2(-3)+1 \\ f\mleft(-3\mright)=-6+1 \\ f\mleft(-3\mright)=-5 \end{gathered}[/tex]
Hence, we have a hollow dot at (-3, -5).
For x = 4, replace "x" with 4 in the second function.
[tex]\begin{gathered} f(x)=2x+1 \\ f(4)=2(4)+1 \\ f(4)=8+1 \\ f(4)=9 \end{gathered}[/tex]
Hence, we have another hollow dot at (4, 9).
Let's plot these hollow dots in the graph and connect them. Here's the graph of the second function.
Lastly, for the third function f(x) = -2 when x ≥ 4. Plot a solid dot at (4, -2) and extend the line infinitely to the right since the inequality is greater than.
The graph of the third function is:
So, combining the three graphs in one plane, the graph of the given piecewise function is: (Final Answer)
