Prior to taking calculus, students must contend with equations. Once they reach that higher level of math, however, they learn a new mathematical construct. A function associates one and only one value in a set called the "domain" with a value in another set called the "range." A function tends to be more restricted than an equation. For example, y^2 = x + 1 is an equation, but not a function. If x = 3, y can be either 2 or -2. You can display a function numerically, algebraically or graphically.
Instructions
1. Draw a coordinate system on your graph paper using the straight edge and pencil. Draw a horizontal axis across the middle of the paper and a vertical axis down the middle.
2. Determine your domain. You can use any set of numbers as long as they don't violate the definition of a function. For example, f(x) = 1 / (x - 1) could use any number in its range except 1, which would put a 0 in the denominator of the function, making f(x) undefined.
Domain: 2 < x < 100
3. Select a few values from the domain to plot on the graph. The more complex the function, the more points you will need to plot to capture the the curvature.
Domain f(x) = [2, 3, 4, 5, 6]
4. Input the domain values you selected into the function and calculate the associate range values. Plot the domain-range pairs on the graph using the x-axis for the domain and the y-axis for the range. For the example function f(x) = 1 / (x - 1):
Domain f(x) = [2, 3, 4, 5, 6]
Range f(x) = [1, 1/2, 1/3, 1/4, 1/5]
5. Align a French curve with the points you plotted and trace a curve that connects all the points.
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