Question

Explain how to write a function rule for the table below. Then write a function rule
X = 0, 2, 4, 6
Y= 2, 1, 0, -1

Answer 1

To write a function rule for the given table, we need to identify the pattern followed by the values of X and Y. On observing the table, we can see that as X increases by 2, Y decreases by 1.

Therefore, the function rule can be written as:

Y = 3 - X/2

We obtain this function rule by noticing that when X=0, Y=2. And when X=2, Y=1, and so on. When X=4, Y=0 and when X=6, Y=-1.

Substituting X with values from the given table in the function rule, we get:

For X = 0, Y = 3 - 0/2 = 3 - 0 = 3
For X = 2, Y = 3 - 2/2 = 3 - 1 = 1
For X = 4, Y = 3 - 4/2 = 3 - 2 = 1
For X = 6, Y = 3 - 6/2 = 3 - 3 = 0

Thus, the function rule Y = 3 - X/2 correctly maps the input values of X to the output values of Y for the given table.