Question

what does the transformation $f(x) \mapsto f(x - 8) - 3$ do to the graph of $f(x)$?
translates it 8 units left and 3 units up
translates it 8 units left and 3 units down
translates it 8 units right and 3 units down
translates it 8 units right and 3 units up

Explanation:

Step1: Analyze horizontal shift

For $f(x-h)$, $h>0$ shifts right 8 units: $f(x-8)$

Step2: Analyze vertical shift

For $f(x)-k$, $k>0$ shifts down 3 units: $f(x-8)-3$

Answer:

translates it 8 units right and 3 units down