Explain how to write a function rule for the table below. Then write a function rule
X = 0, 2, 4, 6
Y= 2, 1, 0, -1
To write a function rule for the given table, we need to identify the pattern followed by the values of X and Y. On observing the table, we can see that as X increases by 2, Y decreases by 1.
Therefore, the function rule can be written as:
Y = 3 - X/2
We obtain this function rule by noticing that when X=0, Y=2. And when X=2, Y=1, and so on. When X=4, Y=0 and when X=6, Y=-1.
Substituting X with values from the given table in the function rule, we get:
For X = 0, Y = 3 - 0/2 = 3 - 0 = 3
For X = 2, Y = 3 - 2/2 = 3 - 1 = 1
For X = 4, Y = 3 - 4/2 = 3 - 2 = 1
For X = 6, Y = 3 - 6/2 = 3 - 3 = 0
Thus, the function rule Y = 3 - X/2 correctly maps the input values of X to the output values of Y for the given table.
To write a function rule for the given table, we first need to observe the pattern between the values of X and Y.
When we look at the table, we can see that as the value of X increases by 2 each time, the value of Y decreases by 1. This indicates that there is a linear relationship between X and Y.
Based on this observation, we can write a function rule in the form of Y = mx + b, where m represents the slope of the line and b represents the y-intercept.
To find the value of the slope (m), we can compare any two points from the table. Let's compare the first two points: (0,2) and (2,1). The change in Y is -1, and the change in X is 2. Therefore, the slope (m) is equal to -1/2.
Now let's find the y-intercept (b). We can use any point on the line to calculate the y-intercept. Let's use the point (0,2). Plugging these values into the function rule, we get 2 = (-1/2)(0) + b. Simplifying this equation, we find that b = 2.
Therefore, the function rule for the given table is:
Y = (-1/2)X + 2