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 this table, we first need to determine the pattern or relationship between the values of X and Y. Looking at the table, we can see that as X increases by 2, Y decreases by 1. This means that there is a constant rate of change of -1/2 (since for every increase of 2 in X, Y decreases by 1).
To write the function rule, we can start with the formula for a linear function: y = mx + b. We know that the rate of change (m) is -1/2, so we can substitute that in: y = (-1/2)x + b. To find the y-intercept (b), we can use one of the points given in the table. Let's use the point (0,2). This means that when x = 0, y = 2. Substituting these values into the equation, we get:
2 = (-1/2)(0) + b
2 = b
So the function rule is:
y = (-1/2)x + 2
To write a function rule from a table, we need to identify the pattern and relationship between the X and Y values.
Looking at the table:
X 0, 2, 4, 6
Y 2, 1, 0, -1
We can observe that as the X values increase by 2 each time, the Y values decrease by 1 each time.
To write a function rule, we can determine the relationship between X and Y. From the table, it can be seen that for every increase of 2 in X value, there is a decrease of 1 in the Y value.
So, the function rule can be written as:
Y = -0.5X + 2
To write a function rule from a table, you need to identify the relationship between the values in the X column and the corresponding values in the Y column.
In this case, let's examine the relationship between X and Y:
When X increases by 2, Y decreases by 1.
From this, we can infer that for every increase of 2 in X, there is a decrease of 1 in Y. This tells us that the slope of the function is -1/2.
To find the vertical intercept, we can observe that when X is 0, Y is 2.
Now, we have enough information to write the function rule:
The function rule for this table is:
Y = -1/2 X + 2
This function rule represents the relationship between X and Y in the given table.