Question

Which of the following statements is true about the relationship between any point on a function, f(x)
, and −f(x)
?(1 point)
Responses

If (x, y)
is on f(x)
, then (−x, −y)
is on −f(x)
.
If (x, y)
is on f of x, then (−x, −y)
is on negative f times x.

If (x, y)
is on f(x)
, then (−x, y)
is on −f(x)
.
If (x, y)
is on f of x, then (−x, y)
is on negative f times x.

If (x, y)
is on f(x)
, then (x, −y)
is on −f(x)
.
If (x, y)
is on f of x, then (x, −y)
is on negative f times x.

If (x, y)
is on f(x)
, then (x, y)
is on −f(x)
.

Answer 1

To understand the relationship between a function \( f(x) \) and its negative \( -f(x) \), let’s analyze what it means for a point \( (x, y) \) to lie on the graph of a function.

1. If a point \( (x, y) \) is on the graph of \( f(x) \), it means that \( y = f(x) \).
2. The negative of the function, \( -f(x) \), means we take the original output and negate it. Hence, for the graph of \( -f(x) \), if \( x \) is the same, then the output will be \( -y \).

Thus, if \( (x, y) \) is on the graph of \( f(x) \), then the corresponding point on the graph of \( -f(x) \) would be \( (x, -y) \).

Based on this reasoning, the correct statement is:

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