4. Graphing a Function Rule
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Substitute some arbitrary values for x to find their corresponding y-values.
One way to graph a function rule is by making a table of values and substituting some arbitrary values for x. Doing so will give the corresponding values of y, which we can use to form ( x, y) coordinate pairs.
| x | 3x^3 | y | (x,y) |
|---|---|---|---|
| -2 | 3( -2)^3 | -24 | ( -2, -24) |
| -1 | 3( -1)^3 | -3 | ( -1, -3) |
| 0 | 3( 0)^3 | 0 | ( 0, 0) |
| 1 | 3( 1)^3 | 3 | ( 1, 3) |
| 2 | 3( 2)^3 | 24 | ( 2, 24) |
By connecting all of our points, we form the graph of the function rule. Because there is a variable with an exponent in the function, our line will not be straight. Later, we will learn that this type of function is called a cubic function.