Question

If the point (7, 43) is on the graph of f(x), what point must be on the graph of - f(-x)? (1 point)
• (7,-43)
• (7,43)
• (-7,13)
• (-7,-43)

Answer 1

To determine a point on the graph of \(-f(-x)\) given that the point \((7, 43)\) is on the graph of \(f(x)\), we can follow these steps:

1. The point \((7, 43)\) means that \(f(7) = 43\).
2. We need to evaluate \(-f(-x)\). First, replace \(x\) with \(-7\) to find the corresponding point:
- The output will be \(-f(-(-7)) = -f(7)\).
3. Since \(f(7) = 43\), we find:
\(-f(7) = -43\).
4. Therefore, the point that corresponds to \(-f(-(-7))\) or \(-f(7)\) is \((-7, -43)\).

So, the point that must be on the graph of \(-f(-x)\) is \((-7, -43)\).

**Answer: (-7, -43)**