Question

9 when you multiply a function by -1, what is the effect on its graph? a. the graph flips over the x - axis. b. the graph flips over the y - axis. c. the graph flips over the line y = x.

Explanation:

To determine the effect of multiplying a function by -1 on its graph, we analyze each option:

• Option A: When a function \( y = f(x) \) is multiplied by -1, we get \( y = -f(x) \). For any point \( (x, y) \) on the original graph, the corresponding point on the new graph is \( (x, -y) \). This is the definition of a reflection over the x - axis (since reflecting a point \( (x,y) \) over the x - axis gives \( (x, -y) \)).
• Option B: A reflection over the y - axis is given by \( y=f(-x) \), not by multiplying the function by -1.
• Option C: A reflection over the line \( y = x \) is the inverse function, which is a different transformation from multiplying the function by -1.

Answer:

A. The graph flips over the x - axis