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 the given table, we need to identify the relationship between the input variable (X) and the output variable (Y).
Notice that as X increases by 2, Y decreases by 1. So, we can say that Y is decreasing by 1 for every 2 units of increase in X.
Thus, the function rule can be written as: Y = -0.5X + 2.
To test this rule, substitute the given X values into the formula and verify that the corresponding Y values match the given table.
For example, when X = 0, Y = -0.5(0) + 2 = 2. When X = 2, Y = -0.5(2) + 2 = 1, and so on.
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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
write a function rule for the given table
x 0, 2, 4, 6,
y 2, 1, 0, -1
To write a function rule, we need to identify the pattern or relationship between the input variable (x) and the output variable (y).
Notice that as x increases by 2, y decreases by 1. So, we can say that for every increase of 2 in x, y decreases by 1. We can also see that when x is 0, y is 2. Therefore, the function rule can be written as:
y = -0.5x + 2
To verify this function rule, we can substitute the given x values into the formula and see if the resulting y values match the values in the table. For example, when x is 0, y should be 2. Substituting x=0 into the function rule, we get:
y = -0.5(0) + 2 = 2
This matches the corresponding value in the table. Similarly, we can check the remaining values in the table and confirm that they match the function rule.
To write a function rule from a table, we need to analyze the pattern or relationship between the values of X and Y. Observing the table, we can see that as the value of X increases by 2, the value of Y decreases by 1. This suggests that there is a linear relationship between X and Y, where the Y value decreases by 1 every time the X value increases by 2.
To write a function rule, we need to express this relationship algebraically. The general form of a linear function is Y = mx + b, where m is the slope of the line and b is the y-intercept.
In this case, since the Y value decreases by 1 every time the X value increases by 2, the slope (m) is -1/2. The negative sign indicates that the line is decreasing, and the fraction -1/2 shows that for every increase in X by 2, the corresponding Y value decreases by 1.
To find the y-intercept (b), we can choose any point from the table. Looking at the table, when X is 0, Y is 2. Therefore, the y-intercept is 2.
Now, we can write the function rule:
Y = -1/2X + 2
This function rule represents the relationship between X and Y in the given table.