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 | 2x+4 | y | (x,y) |
|---|---|---|---|
| -1 | 2( -1) + 4 | 2 | ( -1, 2) |
| 0 | 2( 0) + 4 | 4 | ( 0, 4) |
| 1 | 2( 1) + 4 | 6 | ( 1, 6) |
Let's plot these points on a coordinate plane.
By connecting all of our points with a line, we form the graph of the function rule.
Notice that we substituted some arbitrary values into a table of values for x to find the corresponding values of y. Now, let's assume that the given function rule describes a real-world relationship. As an example, let's look at a fair booth.
As we can see in the picture, for 1 dollar we can get 2 apples, but we always get 4 apples as a bonus. Notice that function rule 2x+4 represents this relationship. In this example negative values does not make sens. Because of this all of the values we substitute should be nonnegative.
| x | 2x+4 | y | (x,y) |
|---|---|---|---|
| 0 | 2( 0) + 4 | 4 | ( 0, 4) |
| 1 | 2( 1) + 4 | 6 | ( 1, 6) |
| 2 | 2( 2) + 4 | 8 | ( 2, 8) |
Keep in mind that it is helpful to think about what input values make sense in each example before making the graph.