Question

Consider the following graph of function f.

Answer 1

The graphed function f(x) is |x - 3 | + 1

To convert f (x) = |x - 3| + 1 into g (x) = |x + 4| - 4 you need to add 7 units to the argument (x) and subract 5 units to the function f(x), as it is shown below.

|x - 3 + 7| = |x + 4|

|x + 4| + 1 - 5 = |x + 4| - 4

Now you should use the fact that adding 7 units to the argument shifts the function 7 units to the left and subtracting 5 units from the function shifts the graph 5 units down.

So the answers are:

a  horizontal shift left 7 units, and a vertical down shift 5 units.