Question

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Find the function rule.

x –2 –1 0 1 2
y 9 4 –1 –6 –11
..

Answer 1

To find the function rule, we can examine how the output (y) values change as the input (x) values change. From –2 to –1, the output decreases by 5. From –1 to 0, the output decreases by 5 again. This pattern continues throughout the table, with the output decreasing by 5 each time the input is increased by 1. Therefore, we can write the function rule as:

y = –5x + k

To find the value of k, we can choose any point from the table and substitute its coordinates into the equation. For example, using the point (0, –1):

–1 = –5(0) + k

–1 = k

So the function rule for this table is:

y = –5x – 1