I need to explain how to write a function rule from the table below and also write a function rule for this table:

x: 2 4 6
y: 1 0 –1

How do you do this?

done by Steve last month

http://www.jiskha.com/display.cgi?id=1366132360

To write a function rule from a table, you need to identify the pattern or relationship between the values of the x-column and the corresponding values of the y-column. Here's how you can do it step-by-step:

Step 1: Examine the relationship between x and y values.
Look for a consistent change or pattern between the x and y values. In this table, it can be observed that for every increase of 2 in the x-values, the y-values decrease by 1.

Step 2: Determine the constant rate of change.
To determine the constant rate of change, you divide the change in the y-values by the change in the x-values. In this table, the change in the y-values is -1 (from 1 to 0, and from 0 to -1), and the change in the x-values is 2 (from 2 to 4, and from 4 to 6). Dividing -1 by 2 gives you a constant rate of change of -0.5.

Step 3: Write the function rule.
Since the constant rate of change is -0.5, it means that for every increase of 1 in the x-values, the y-values decrease by 0.5. You can express this as a function rule.

In this case, the function rule is:
y = -0.5x + b

However, we need to find the value of b (the y-intercept) to complete the function rule. To do this, we can use one of the points from the table, such as (2, 1). We can substitute this x and y value into the equation and solve for b.

1 = -0.5(2) + b
1 = -1 + b
b = 2

Therefore, the function rule for this table is:
y = -0.5x + 2

To write a function rule from a given table, you need to observe the pattern or relationship between the input values (x) and the corresponding output values (y). In this case, let's examine the given table:

x: 2 4 6
y: 1 0 -1

From the table, we can see that as the value of x increases by 2 each time, the value of y decreases by 1. This suggests that the function rule is likely to involve subtraction.

To write the function rule, we can start by considering the constant change between the input values. In this case, the constant change is -1, as y decreases by 1 when x increases by 2. This means that the function involves subtracting 1 from the input value.

Next, we need to find the initial value (y-intercept) for the function. To do this, we can observe the value of y when x is 0 (since there is no 0 in the given table, we can use a value from the table as a reference). Here, when x is 2, y is 1. So, we can conclude that when x is 0, y should be 3.

Putting it all together, the function rule for this table can be written as:

f(x) = -1x + 3

Or, the function rule can be written as:

y = -x + 3