Question

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

Explanation:

Step1: Recall horizontal shift rule

For a function \( y = f(x) \), the transformation \( y = f(x + h) \) (where \( h>0 \)) shifts the graph horizontally. The rule is: if \( h>0 \), the graph shifts \( h \) units to the left; if \( h < 0 \), it shifts \( |h| \) units to the right.

Step2: Apply the rule to \( f(x)\to f(x + 4) \)

Here, \( h = 4>0 \). So according to the horizontal shift rule, the graph of \( f(x) \) will be translated 4 units to the left.

Answer:

translates it 4 units left