18. 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
To write a function rule from a table, we need to analyze the pattern between the input (x) and the output (y) values. In this case, we can observe that as x increases by 2, y decreases by 1. Therefore, we can say that the relationship between x and y is that y decreases by 0.5 for every 1 increase in x.
Using this information, we can write a function rule:
y = -0.5x + 2
This says that y is equal to negative 0.5 times x, plus 2. We can test this function rule by plugging in the x values from the table:
- When x is 0: y = -0.5(0) + 2 = 2
- When x is 2: y = -0.5(2) + 2 = 1
- When x is 4: y = -0.5(4) + 2 = 0
- When x is 6: y = -0.5(6) + 2 = -1
These output values match the y values from the table, confirming that our function rule is correct.