To determine whether [tex]\( f(x) \)[/tex] is a function, we need to verify whether each input (or [tex]\( x \)[/tex]-value) maps to exactly one output (or [tex]\( y \)[/tex]-value). This can be tested using the vertical line test.
Vertical Line Test: A graphical method to determine if a relation is a function. According to this test, if a vertical line drawn anywhere on the graph intersects the graph at more than one point, the relation is not a function.
To check [tex]\( f(x) \)[/tex]:
1. Analyze the relationship visually: Imagine drawing vertical lines across the graph of [tex]\( f(x) \)[/tex].
2. Vertical Line Intersection: Look to see if any vertical line intersects the graph at more than one point.
If any vertical line intersects the graph at more than one point, then the relation is not a function. If no vertical line intersects the graph at more than one point, then the relation is indeed a function.
Given the context and analysis:
The plot of [tex]\( f(x) \)[/tex] does not violate the vertical line test. Hence, it can be concluded that [tex]\( f(x) \)[/tex] is a function.
Therefore, the answer is:
A. True
