What is the funtion rule shown in the table
n 3,4,5,6
y 2,1,0,-1
I will let n = x.
Take two points. For instance, the first two points, (3,2) and (4,1).
Get the slope:
m = (y2 - y1) / (x2 - x1)
m = (2 - 1) / (3 - 4)
m = 1 / -1
m = -1
slope-intercept form:
y - y1 = m(x - x1)
y - 2 = -1(x - 3)
y - 2 = -x + 3
y = -x + 3 + 2
y = -x + 5
hope this helps~ `u`
To determine the function rule shown in the table, we need to analyze how the values of "n" relate to the corresponding values of "y".
Looking at the values of "n" and "y" in the table:
n: 3, 4, 5, 6
y: 2, 1, 0, -1
We can notice that as "n" increases by 1, "y" decreases by 1. This suggests that the function rule is a linear relationship with a negative slope.
To find the exact function rule, we can calculate the difference in "y" values for each consecutive "n" value:
Difference in "y" (Δy):
-1 - 0 = -1
0 - 1 = -1
1 - 2 = -1
We observe that the difference in "y" values (Δy) is always -1.
Thus, the function rule can be written as:
y = -1n + c
where "c" represents a constant term.
To find the value of "c", we substitute one set of "n" and "y" values into the function rule. Let's use (3, 2):
2 = -1(3) + c
2 = -3 + c
Now, we can solve for "c":
2 + 3 = c
c = 5
Therefore, the function rule shown in the table is:
y = -1n + 5
To determine the function rule shown in the table, we need to identify the relationship between the values of "n" and "y".
Looking at the values of "n" and "y" in the table:
n: 3, 4, 5, 6
y: 2, 1, 0, -1
We can observe that as the value of "n" increases by 1, the value of "y" decreases by 1.
Therefore, the function rule can be described as "y = 2 - (n - 3)", where "n" represents the input value and "y" represents the output value.
To get to this rule, we subtract 3 from "n" since the first value of "n" in the table is 3, and we start our function rule similarly with 3. Then, we subtract "n - 3" from 2 to determine the corresponding value of "y".
Now, if you input any value of "n" into the function rule "y = 2 - (n - 3)", you can calculate the corresponding value of "y".