What is the effect of multiplying a function by a negative constant on its graph

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Question: What is the effect of multiplying a function by a negative constant on its graph?

Options:

Correct Answer: It reflects the graph across the x-axis.

Solution:

Multiplying a function by a negative constant reflects the graph across the x-axis.

What is the effect of multiplying a function by a negative constant on its graph?

What is the effect of multiplying a function by a negative constant on its graph?

Step 1: Start with a function, for example, f(x). This is the original graph you want to analyze.
Step 2: Multiply the function by a negative constant, like -1. This gives you a new function, g(x) = -f(x).
Step 3: Understand what happens to the points on the graph of f(x). If a point is at (x, y), it will now be at (x, -y) on the graph of g(x).
Step 4: Notice that the y-values of all points on the graph are flipped. Positive y-values become negative, and negative y-values become positive.
Step 5: This flipping of y-values means that the entire graph is reflected across the x-axis.

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