Explain how to write a function rule from the table below. The write a function rule.
X 2,4,6
Y 1,0,-1
when x increases by 2, y always decreases by 1
so
m = slope = -1/2
y = -x/2 + b
put in a point like (4,0)
0 = -4/2 + b
so b = 2
so
y = -x/2 + 2
To write a function rule from a table, we need to identify the relationship between the values of X and Y.
Step 1: Analyze the table
Looking at the table, we notice that as the values of X increase by 2, the values of Y decrease by 1.
Step 2: Identify the pattern
From the analysis, we can identify that there is a consistent pattern in the table. For each increase of 2 in X, Y decreases by 1.
Step 3: Write the function rule
To write the function rule, we need to express the relationship between X and Y using mathematical expressions.
In this case, the function rule can be written as follows:
Y = -X/2 + 3
Explanation of the function rule:
- The coefficient of X is -1/2, which represents the rate of change. It indicates that for every increase of 2 in X, Y decreases by 1.
- The constant term 3 represents the y-intercept, which is the value of Y when X is 0. In this case, Y is 3 when X is 0.
Therefore, the function rule for the given table is Y = -X/2 + 3.
To write a function rule from a table, you need to examine the relationship between the input (X) and the corresponding output (Y) values.
Looking at the given table:
X | Y
2 | 1
4 | 0
6 | -1
To find the function rule, you need to determine how the values in the X column are related to the values in the Y column.
In this case, as the X values increase by 2 each time, the Y values decrease by 1 each time. This suggests that there is a constant change or a linear relationship between X and Y.
To write the function rule, you can express this linear relationship in the form of "Y = mx + b," where m represents the slope and b represents the y-intercept.
To determine the slope (m), you can choose any two pairs of X and Y values and calculate the change in Y divided by the change in X.
Let's choose the pairs (2,1) and (4,0):
Change in Y = 0 - 1 = -1
Change in X = 4 - 2 = 2
Slope (m) = Change in Y / Change in X
= -1 / 2
= -0.5
Now, using the slope-intercept form, we can write:
Y = mx + b
Substituting the value of m, we have:
Y = -0.5x + b
To find the y-intercept (b), you can choose one of the points from the table and substitute its corresponding X and Y values into the equation.
Using the point (2,1):
1 = -0.5(2) + b
1 = -1 + b
Solving for b:
1 + 1 = b
2 = b
Now that we have found the value of b, we can substitute it back into the equation:
Y = -0.5x + 2
Therefore, the function rule for the given table is:
Y = -0.5x + 2