explain How to write a function rule from the table below. Then write a funciton rule.
X|Y
0|2
2|1
4|0
6|-1
To write a function rule, we need to identify the relationship between the input values (X) and the output values (Y). Looking at the table, we notice that as X increases by 2, Y decreases by 1. This tells us that the function is a linear function with a slope of -1/2.
Therefore, the function rule can be written as:
Y = -1/2 X + 2
To write a function rule from the given table, we need to identify the pattern or relationship between the values of X and Y.
By examining the table, we can see that as X increases by 2, Y decreases by 1. This implies that the function has a constant rate of change of -1 for each increase of 2 in X.
To write a function rule, we can express this relationship as follows:
- For every increase of 2 in X, Y decreases by 1.
Therefore, the function rule representing this relationship is:
Y = -1/2 * X + b
To determine the constant term, b, we can substitute the values from the table into the function rule. Let's use the first row from the table where X = 0 and Y = 2. Substituting these values into the equation, we can solve for b:
2 = -1/2 * 0 + b
2 = 0 + b
b = 2
So, the function rule for the given table is:
Y = -1/2 * X + 2