Question

which transformation transforms the graph of f(x) = x² to the graph of g(x) = (x + 4)²?
options:
a horizontal translation 4 units to the left
a vertical translation 4 units up
a vertical translation 4 units down
a horizontal translation 4 units to the right

Explanation:

Step1: Recall horizontal shift rule

For $f(x) = x^2$, $g(x)=f(x+h)$ shifts left by $h$ units.

Step2: Match given function to rule

Here $h=4$, so $g(x)=(x+4)^2=f(x+4)$.

Answer:

a horizontal translation 4 units to the left