Question

Graph
`fx= |x+1| +2`

Answer 1

The graph is shown in the following image

Explanation:

The parent function of
`f(x) = | x + 1 | +2` is
`y = | x |`

The graph of
`y = | x |` is the union of two lines:

`y = x` for
`x\geq0`

`y = -x` for
`x <0`

The vertex of this graph is in point (0,0)

The graphic is shown in the attached image.

Then, if we do
`y = f(x + 1)` to the parent function we get:

`y = | x + 1 |`

This transformation shifts the graph of
`y = |x|` 1 unit to the left

Then, if we make the transformation
`y = f(x) + 2` to the function
`y = | x + 1 |` we obtain:

`y = | x + 1 | +2`

This transformation displaces the graph of the function
`y = | x + 1 |` 2 units up on the y axis.

So, if the vertex of the main function
`y = | x |` was at point (0,0), the vertex of the function
`f(x) = |x + 1| +2` has its vertex in the point (-1, 2).

The graph is shown in the following image