To solve for the function, let x and y represent the inputs and outputs, respectively.
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:
For (1,3) and (3,1), its slope is:
And, for (3,1) and (4,0), the slope is:
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:
Plug-in the slope m=-1 and the y-intercept b=4 to the formula.
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` .