What are the steps to performing the following transformation and then graphing it?

Transformation: compress f(x) = |2x| - 3 vertically by a factor of 1/4.

g(x) = f(x)/4 = |x/2| - 3/4

See

http://www.wolframalpha.com/input/?i=plot+y%3D|2x|-3%2C+y%3D|x%2F2|+-+3%2F4

To perform the transformation and graph the compressed function, follow these steps:

1. Start with the original function: f(x) = |2x| - 3.

2. Apply the vertical compression by a factor of 1/4. To compress the function vertically, multiply the function's output (y-values) by the compression factor. In this case, multiply the function's output by 1/4.

Compressed function: g(x) = (1/4)(|2x| - 3).

3. Simplify the compressed function. Multiply the compression factor into the function expression.

g(x) = (1/4)|2x| - (1/4)(3).

g(x) = (1/4)|2x| - 3/4.

4. Graph the compressed function. To graph the function, plot several points and connect them to get a clear picture of the compressed function's shape.

- Choose values for x and calculate corresponding y-values for the compressed function.
- Start with a few values, such as x = -2, -1, 0, 1, and 2.
- Plug these x-values into the compressed function, g(x), to get the corresponding y-values.
- Plot the points (x, g(x)) on the graph.

For example:
- For x = -2, g(-2) = (1/4)|2(-2)| - 3/4 = (1/4)(4) - 3/4 = 1 - 3/4 = 1/4.
- So, the point (-2, 1/4) is plotted on the graph.

Continue this process for the chosen values of x to get several points. Connect these points smoothly to complete the graph.

5. Label the axes and add any other necessary information, such as the function's name (g(x)) and the scale.

That's how you perform the transformation and graph the compressed function.