Question

Choose the correct statement to describe a true relationship between any point on f(x) and f(−x)

Responses

If (x,y) is on the graph of f(x) then (−x,−y) is on the graph of f(−x)


If (x,y) is on the graph of f(x), then (−x,y) is on the graph of f(−x)
If (x,y) is on the graph of f(x), then (x,−y) is on the graph of f(−x)

If (x,y)is on the graph of f(x) then (x,y) is on the graph of f(−x)

Answer 1

The correct statement to describe the relationship between any point on \( f(x) \) and \( f(-x) \) is:

**If (x, y) is on the graph of f(x), then (−x, y) is on the graph of f(−x)**.

This means that if you have a point on the graph of \( f(x) \) at \( (x, y) \), the corresponding point on the graph of \( f(-x) \) will be \( (-x, y) \).

This reflects the property of even functions, where \( f(-x) = f(x) \), and the graph is symmetric with respect to the y-axis.