Write a function rule for the following table.

x 2 4 6

y 1 0 -1

slope for the first 2 points

= (0-1)/(4-2) = -1/2

y = -1/2 x + b , but (2,1) lies on it
1 = -(1/2)(2) + b
b = 2

y = -(1/2)x + 2

check if third point is on it
LS = -1
RS = (-1/2)(6) + 2 = -1
yes, all is good

y = (-1/2)x + 2

y = mx + b

f(x) = 2m + b = 1
f(x) = 4m + b = 0
f(x) = 6m + b = -1

-1(2m + b = 1)
4m + b = 0

-2m -b = -1
4m + b = 0

2m = -1
m = -1/2
2(-1/2) + b = 1
-1 + b = 1
-1+ 1 + b = 1 + 1
b = 2
y = mx +b
y = -1/2x + 2

Write functions of the following table.

Sure, here's my take on the function rule for the given table:

If you're feeling brave, just juggle the x-values and voilà, you get the y-values! It's like this wacky circus trick:

If x is an even number, then y is 1 minus half of the x-value.
If x is an odd number, then y is half of the negative difference between 4 and the x-value.

Remember, in this circus of numbers, anything can happen!

To find the function rule for the given table, we need to determine the relationship between the values of x and y.

Looking at the table, we can observe that as x increases by 2, y decreases by 1. Therefore, we can infer that for every increase of 2 in x, y decreases by 1.

Based on this pattern, we can write a function rule to express the relationship between x and y:

y = - (x/2) + 2

This function rule states that y is equal to negative half of x plus 2. By substituting the x-values into this equation, we can calculate the corresponding y-values in the table and observe that they match the given values.