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How to Make a Graph Shift

A mathematical function provides the means to manipulate input data, and generate an output. The range of mathematical functions includes sinusoidal and exponential forms. Sometimes it is useful to manipulate graphs of functions by moving them to another area of the x-y coordinate plane. This can be done by transforming the function.

Things You'll Need

Graph paper

Instructions

- 1
  Write down the mathematical function that needs to be moved. For example, the function may be the periodic function sin(x) : y = sin(x)
- 2
  Write down the transformed mathematical function. An arbitrary mathematical function can be moved by "a" in the x-direction and "b" in the y-direction using the following formula: y = f(x - a) + b. For example, if the graph is to be moved to the right by 5 units and up by 10 units, the transformation on y = sin(x) would be y = sin(x - 5) + 10.
- 3
  Plot the graph. Place a number of values into the transformed function to generate values for "x" and "y." Plot each pair of x and y values on the graph by placing a cross at their coordinates. Using a ruler, draw lines between adjacent points. The graph should appear to be moved.

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