Answer:
The graph is shown in the following image
Step-by-step explanation:
The parent function of [tex]f(x) = | x + 1 | +2[/tex] is [tex]y = | x |[/tex]
The graph of [tex]y = | x |[/tex] is the union of two lines:
[tex]y = x[/tex] for [tex]x\geq0[/tex]
[tex]y = -x[/tex] for [tex]x <0[/tex]
The vertex of this graph is in point (0,0)
The graphic is shown in the attached image.
Then, if we do [tex]y = f(x + 1)[/tex] to the parent function we get:
[tex]y = | x + 1 |[/tex]
This transformation shifts the graph of [tex]y = |x|[/tex] 1 unit to the left
Then, if we make the transformation [tex]y = f(x) + 2[/tex] to the function [tex]y = | x + 1 |[/tex] we obtain:
[tex]y = | x + 1 | +2[/tex]
This transformation displaces the graph of the function [tex]y = | x + 1 |[/tex] 2 units up on the y axis.
So, if the vertex of the main function [tex]y = | x |[/tex] was at point (0,0), the vertex of the function [tex]f(x) = |x + 1| +2[/tex] has its vertex in the point (-1, 2).
The graph is shown in the following image
