To determine how the graph of the function [tex]\( f(x) = x^2 \)[/tex] has been translated, let's analyze the function [tex]\( f(x) = x^2 - 9 \)[/tex].
First, recall the parent function:
[tex]\[ f(x) = x^2 \][/tex]
This function represents a standard parabola that opens upwards with its vertex at the origin [tex]\((0, 0)\)[/tex].
Next, consider the given function:
[tex]\[ f(x) = x^2 - 9 \][/tex]
When comparing this to the parent function [tex]\( f(x) = x^2 \)[/tex], it's evident that we are subtracting 9 from the output of the function.
Subtracting a constant from the function causes a vertical translation of the graph. Specifically, subtracting 9 means every point on the graph of [tex]\( f(x) = x^2 \)[/tex] is moved 9 units downward.
Thus, the transformation that has occurred is a vertical translation of 9 units down.
### Answer:
B) It has been translated 9 units down.
