What is the rule for a function with inputs, 0,1,3,4 and outputs 4,3,1,0?

lemjay | Certified Educator

To solve for the function, let x and y represent the inputs and outputs, respectively.

x       y

0       4

1       3

3       1

4       0

Now that the corresponding values of y for each x value are known, it indicates that the function contain the points (0,4) , (1,3) , (3,1) and (4,0).

Next, solve for the slope between two points to determine if the function is linear or not.

For (0,4) and (1,3), the slope is:

`m=(y_2-y_1)/(x_2-x_1)=(3-4)/(1-0)=(-1)/1=-1`

For (1,3) and (3,1), its slope is:

`m=(1-3)/(3-1)=(-2)/2=-1`

And, for (3,1) and (4,0), the slope is:

`m=(0-1)/(4-3)=(-1)/1=-1`

Since their slopes are the same, hence, the function is linear.

Furthermore, the point (0,4) is the y-intercept of the function.

So to determine the function, apply the slope-intercept form which is:

`y=mx+b`

Plug-in the slope m=-1 and the y-intercept b=4 to the formula.

`y=-1*x+4`

`y=-x+4`

And, replace y with f(x) to indicate it as the function of the given inputs and outputs.

Hence, the function is  `f(x)=-x+4` .