How do you graph the function #f(x)=absx+2# and its inverse?

The parent function #f(x) = |x|# looks like:

graph{|x| [-9.06, 8.72, -2.36, 6.53]}

Move the vertex to #(0,2)#:

graph{|x|+2 [-10.17, 9.83, -2.916, 7.085]}

or do point-plotting: #(-3,5), (-1, 3), (0, 2), (1, 3), (3, 5), (5, 7)...#

The inverse can be created a number of ways.
One way is to reverse the #x# and #y#'s and plot the reversed points. But you need to realize in order to have an inverse, the original function must be limited in its' domain. To be a function of #x# the function must pass both the vertical and horizontal line test. To pass the horizontal line test, the original function must limit its' domain to #x >= 0#. This means the #y# values of the inverse function must be limited to #y>=0#
Inverse function's points for point plotting: #(2, 0), (3, 1), (5, 3), (7, 5), ...#

A 2nd way to find the inverse function is to
1. Make #f(x) = y#: #y = |x| + 2#
2. Switch #x# and #y#: #x = |y| + 2#
3. Solve for #y: |y| =x - 2#
4. For #y >= 0: y = x - 2#

Note: The inverse function is always mirrored about the #y = x# axis.