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Consider the function . What happens to the graph if we multiply the output of this function by a constant? For example, what will the graph of , or , look like?

Use the tool to multiply the output of the function by different values. How does the graph of the function af(x) compare to the graph of f(x)? What remains the same? What changes? Click "Done Exploring" when finished.

When you multiply f(x) by a constant, a, the graph of f(x) is stretched vertically. The x-intercepts remain fixed because the y-value of these points is 0, which doesn't change when you multiply it by a constant.

What happens if you multiply a function by a negative value?

Use the "-a" button to multiply f(x) by a negative constant. How is the graph affected? Click "Done Exploring" when finished.

You can think of a transformation such as -2f(x) as a combination of two separate transformations. First, the graph is stretched vertically by a factor of 2, then it is reflected across the x-axis.

The vertical stretches and compressions you have studied so far are summarized to the right.

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