Question

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

1. (7, -43)
2. (-7, -43)
3. (-7, 43)
4. (7, 43)

Answer 1

To find the point that must be on the graph of \( -f(-x) \) given that the point \( (7, 43) \) is on the graph of \( f(x) \), we need to follow these transformations step by step:

1. The point \( (7, 43) \) means \( f(7) = 43 \).

2. To find \( -f(-x) \), we need to first evaluate \( f(-x) \). Since we are given \( f(7) \), let's find the corresponding input for \( -x \):

- For \( x = 7 \), \( -x = -7 \). Thus, \( f(-7) = f(7) = 43 \).

3. The next step is to take the negative of this result:

- Therefore, \( -f(-7) = -43 \).

4. Thus, we have \( -f(-x) \) evaluated at \( x = 7 \) gives us:

- The point corresponding to this transformation is \( (-7, -43) \).

So, the correct answer is:

**2. (-7, -43)**.