Question

If the point (13,−7)

is on the graph of f(x), what point must be on the graph of f(−x)

Responses

The point (−13,−7) must be on the graph of f(−x)

The point (13,7) must be on the graph of f(−x)

The point (−13,7) must be on the graph of f(−x)

The point (13,−7) must be on the graph of f(−x)

Answer 1

To understand how the graph of \( f(-x) \) relates to the graph of \( f(x) \), we can analyze the transformation involved.

The point \( (13, -7) \) means that \( f(13) = -7 \). When we consider \( f(-x) \), we need to replace \( x \) with its negative counterpart.

For the x-coordinate of the original point \( (13, -7) \):

- The input \( x = 13 \) in \( f(x) \) becomes \( x = -13 \) in \( f(-x) \).

The output \( f(-x) \) will therefore be \( f(-(-13)) = f(13) \).

Since we established that \( f(13) = -7 \), we now have:

- For \( x = -13 \) in \( f(-x) \), the corresponding output is \( f(-13) = -7 \).

Thus, the point \( (-13, -7) \) must be on the graph of \( f(-x) \).

So, the correct response is:

**The point (−13,−7) must be on the graph of f(−x).**