I need a function rule for the following:
X Y
-2 -2
0 1
1 2
Well, it's not a straight line, since the change is y is not proportional the change in x. You could fit a very large number of functions to those threee points, but the simplest would be a parabola of the form
y = ax^2 + bx + c
You can use your three data points to solve for a, b and c.
-2 = 4a - 2b + c
1 = c
2 = a + 4b + c
This tells you right away what c is, so now you can solve for a and b
I just need a function rule for the graph. ex. y=2x+1
I know what you are asking for. A function of the form y = mx + b won't fit all three points. That is why I chose a quadratic function. Try completing what I started
To find the function rule that relates the values of X and Y, we can consider the pattern between the given values. Let's use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
The slope (m) can be found by taking the difference in Y-values and dividing it by the difference in X-values. In this case, the difference in Y-values is 2 - (-2) = 4, and the difference in X-values is 1 - 0 = 1. So, the slope is 4/1 = 4.
We can substitute one set of X and Y values into the equation to find the value of the y-intercept (b).
Using the coordinates (0,1), we have:
1 = 4(0) + b
1 = 0 + b
b = 1
Now that we have the slope (4) and the y-intercept (1), we can write the function rule:
Y = 4X + 1
Therefore, the function rule that relates the values of X and Y is Y = 4X + 1.