Question

Determine whether the statement is true or false. Justify your answers.

Answer 1

Answer:

The graph of y = f(-x) is a reflection of the graph of y = f(x) in the x-axis. ⇒ False

The graph of y = -f(x) is a reflection of the graph of y = f(x) in the y-axis. ⇒ False

Step-by-step explanation:

Let us explain the reflection about the axes

• If a graph is reflected about the x-axis, then the y-coordinates of all points on it will opposite in sign

Ex: if a point (2, -3) is on the graph of f(x), and f(x) is reflected about the x-axis, then the point will change to (2, 3)

• That means reflection about the x-axis change the sign of y

• y = f(x) → reflection about x-axis → y = -f(x)

• If a graph is reflected about the y-axis, then the x-coordinates of all points on it will opposite in sign

Ex: if a point (-2, -5) is on the graph of f(x), and f(x) is reflected about the y-axis, then the point will change to (2, -5)

• That means reflection about the y-axis change the sign of x

• y = f(x) → reflection about y-axis → y = f(-x)

Now let us answer our question

The graph of y = f(-x) is a reflection of the graph of y = f(x) in the x-axis.

It is False because reflection about x-axis change sign of y

The graph of y = -f(x) is a reflection of the graph of y = f(x) in the x-axis

The graph of y = -f(x) is a reflection of the graph of y = f(x) in the y-axis.

It is False because reflection about y-axis change sign of x

The graph of y = f(-x) is a reflection of the graph of y = f(x) in the y-axis