Question

Choose the statement the best describes a true relationship between any point of f of x and negative f of negative X

Answer 1

The statement that best describes the relationship between \( f(x) \) and \( -f(-x) \) is:

**The points of the function \( f(x) \) and the points of the function \( -f(-x) \) are symmetrically located with respect to the origin.**

This means that if you take a point \( (a, f(a)) \) on the graph of \( f(x) \), there will be a corresponding point \( (-a, -f(-a)) \) on the graph of \( -f(-x) \). This indicates that \( -f(-x) \) is the reflection of \( f(x) \) in both axes, where the x-coordinates are negated and the y-coordinates are also negated. In other words, \( -f(-x) \) represents a transformation of \( f(x) \) involving a horizontal flip (negating the x-values) and a vertical flip (negating the y-values).