Find the function rule
(-2,9) (-1,4) (0,-1) (1,-6) (2,-11)
I think the function rule is you subtract 5 from the y as you go on.
y = - ( 5 x + 1 )
x = - 2
y = - [ 5 * ( - 2 ) + 1 ] = - ( - 10 + 1 ) = - ( - 9 ) = 9
x = - 1
y = - [ 5 * ( - 1 ) + 1 ] = - ( - 5 + 1 ) = - ( - 4 ) = 4
x = 0
y = - ( 5 * 0 + 1 ) = - ( 0 + 1 ) = - 1
x = 1
y = - ( 5 * 1 + 1 ) = - ( 5 + 1 ) = - 6
x = 2
y = - ( 5 * 2 + 1 ) = - ( 10 + 1 ) = - 11
Of course you can write:
- ( 5 x + 1 ) = - 5 x -1
To find the function rule for the given set of points, let's analyze the pattern between the x and y-values.
When we move from (-2, 9) to (-1, 4), we can see that the x-value increases by 1 and the y-value decreases by 5. Similarly, when we move from (-1, 4) to (0, -1), the x-value increases by 1, and the y-value decreases by 5.
This pattern continues consistently for all the given points. Therefore, we can conclude that the function rule is to subtract 5 from the y-value as you increase the x-value by 1.
The function rule can be expressed as:
y = -5x + c
To find the constant term 'c,' we can substitute the x and y-values of any point. Let's use the point (-2, 9):
9 = -5(-2) + c
9 = 10 + c
c = 9 - 10
c = -1
Therefore, the function rule for the given set of points is:
y = -5x - 1
To determine the function rule based on the given set of coordinate points, we need to examine the relationship between the x-values and the y-values. Let's analyze the given points:
(-2,9) (-1,4) (0,-1) (1,-6) (2,-11)
As we observe, the y-values (values in the second position) are decreasing by 5 units as the x-values (values in the first position) increase by 1 unit. Based on this pattern, it seems like subtracting 5 from the y-value for each increase of 1 in the x-value might be the function rule.
So, you are correct in thinking that the function rule subtracts 5 from the y-value for each increase of 1 in the x-value. The function rule can be expressed as follows:
f(x) = y - 5
Alternatively, you can also express it as:
y = x - 5
These equations represent the rule you identified, where you subtract 5 from the y-value to get the next y-value as x increases by 1 unit.