Question

Graphn="absmiddle" class="latex-formula">

Answer 1

Answer:

The graph is shown in the following image

Step-by-step 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    $x$

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