The representation table given indicates that the function is linear, as the difference between consecutive y-values (9-8, 8-7, and 7-6) is constant. Therefore, we can represent the function with a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.
To find the equation of the function, we can use the x- and y-values given in the table to solve for m and b. For example, using the x- and y-values (-3,9) and (-2,8), we can solve the equation 9 = m(-3) + b for m and b:
9 = -3m + b
8 = -2m + b
Subtracting the second equation from the first equation gives us:
1 = -m
So the slope of the function is -1. Substituting this value back into either equation gives us:
9 = -3(-1) + b
9 = 3 + b
6 = b
So the y-intercept of the function is 6. Therefore, the equation of the function is y = -1x + 6.
The other two representations can be solved in the same way to find the equations of those functions.