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

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

When you multiply the input of f(x) by a constant, b, the graph of f(x) is stretched horizontally. Only the y-intercepts remain fixed.

What happens if b is negative?

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

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

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

Select the equation which best describes the transformation: "f(x) is reflected across the x-axis, shifted to the right 2 units, and shifted up 3 units." Click "Submit" when finished.

The graph of f(x) is shown. Match each graph to an equation. Click "Submit" when finished.

Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education