From the problem, we have the function :
[tex]f(x)=\lvert x+1\rvert+2[/tex]
Note that an absolute value function is in V-shape and the vertex will be (h, k) :
[tex]f(x)=\lvert x-h\rvert+k[/tex]
The vertex is at (-1, 2) and we need another two points to graph this function.
[tex]\begin{gathered} \text{when x = }2 \\ f(2)=|2+1|+2 \\ f(2)=3+2=5_{} \\ \\ \text{when x = -}4 \\ f(-4)=|-4+1|+2 \\ f(-4)=3+2=5 \end{gathered}[/tex]
The points are (2, 5) and (-4, 5) with a vertex at (-1, 2).
Plot the points into the rectangular coordinate system.
The graph will be :
