Question

Kimmie compares the graph of g(x) = |x - 2| - 3 to the graph of f(x) = |x| Which describes the graph of g(x) compared to f(x)

Answer 1

We could start with the simpler function f(x) = IxI and construct the other function using transformations.

First, an horizontal translation of A units to the right is written as:

g(x) = f(x - A)

And an vertical translation of A units up, is written as:

g(x) = f(x) + A.

Where A is positive and this works for any function f(x).

Then in this case, if we start with:

f(x) = IxI and:

g(x) = Ix - 2I -3

Then:

First we do an horizontal translation of 2 units to the right.

g(x) = f(x - 2) = Ix - 2I

Then we do a vertical translation of -3 units up (or a translation of 3 units down)

g(x) = f(x - 2) - 3 = Ix - 2I - 3

Those two transformations are the ones that relate the graphs of g(x) and f(x)