Please could you help me in finding a function rule for the following table:

x: 2 3 4
f(x):2 1 0

The following works. You can reexpress it more simply.

f(x) = x + 2(2 - x)

Oh thanx for the help! I got the function rule as f(x)= 4-x

To find the function rule for the given table, we need to analyze the relationship between the input values (x) and the corresponding output values (f(x)).

Looking at the table, we can observe that as the input value (x) increases by 1, the output value (f(x)) decreases by 1. This suggests a linear relationship, where the output value decreases by 1 for every increase of 1 in the input value.

So, we can write the function rule as:
f(x) = 2 - (x - 2)

Here's how we derived the function rule:

1. Start with the general equation for a linear function: f(x) = mx + b
2. Determine the slope (m) by comparing the change in the output values (f(x)) to the change in the input values (x). In this case, the output decreases by 1 when the input increases by 1, so the slope is -1.
3. Find the y-intercept (b) by substituting the values from the table into the equation and solving for b. Since f(2) = 2, we can substitute x = 2 and f(x) = 2 into the equation:
2 = -1(2) + b
Simplifying the equation, we find b = 4.
4. Substitute the values for m and b into the general equation to get the final function rule:
f(x) = -x + 4

So, the function rule for the given table is f(x) = -x + 4.