Question

Explain how to write a function rule from 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 from a table, look for any patterns or relationships between the input (x) and output (y) values. One way to do this is to see if there is a constant difference or ratio between the values.

In this case, we can see that as x increases by 2 (from 0 to 2 to 4 to 6), y decreases by 1 (from 2 to 1 to 0 to -1). This means that there is a constant difference of -1 between the x and y values.

To write a function rule, we can use the slope-intercept form of a linear equation: y = mx + b. In this case, the slope (m) is equal to the constant difference we found (-1), and the y-intercept (b) is the starting y-value (2).

Therefore, the function rule for this table is:

y = -x + 2