Math related to graphing

Question

A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph.

f(x) = |x|;

 shift downward 9 units and shift 8 units to the left.

Answer 1

Initial function:

f(x) = |x|

Shift downwards 9 units:

f(x) = |x| - 9

Shift 8 units to the left:

f(x) = |x + 8| - 9

You can figure out whether that last step should be "+8" or "-8" by thinking of the "lowest point" of the curve (for what value of x is the curve at its lowest? Is it x = -8 or x = +8 ?).

I hope this helps.