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 | - x^2+2 | y | (x,y) |
|---|---|---|---|
| -2 | -( -2)^2 + 2 | -2 | ( -2, -2) |
| -1 | -( -1)^2 + 2 | 1 | ( -1, 1) |
| 0 | -( 0)^2 + 2 | 2 | ( 0, 2) |
| 1 | -( 1)^2 + 2 | 1 | ( 1, 1) |
| 2 | -( 2)^2 + 2 | -2 | ( 2, -2) |
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 quadratic function, and this type of graph is called a parabola.