Question

what does the transformation $f(x) \mapsto f(x + 10) - 4$ do to the graph of $f(x)$?
translates it 10 units right and 4 units down
translates it 10 units left and 4 units up
translates it 10 units right and 4 units up
translates it 10 units left and 4 units down

Explanation:

Step1: Analyze horizontal shift

For a transformation $f(x) \to f(x + h)$, if $h>0$, the graph shifts left by $h$ units. Here $h=10$, so shift left 10 units.

Step2: Analyze vertical shift

For a transformation $f(x) \to f(x) - k$, if $k>0$, the graph shifts down by $k$ units. Here $k=4$, so shift down 4 units.

Answer:

translates it 10 units left and 4 units down