write a function that relates the input X and the output Y.
1.
input x: -2 0 2 4
output y: 4 0 -4 -8
2.
input x: 0 1 2 3
output y: 1 4 7 10
thanks )
the two input and output tables I made are not really easy to follow. But this is what I meant:
(x,y)
1. (-2, 4), (0,0), (2,-4), (4,-8)
2. (0,1), (1,4), (2,7), (3,10)
To find the function that relates the input X and the output Y, we can calculate the slope (m) and y-intercept (b) using two data points and then write the equation of the line in the form y = mx + b.
1. Using the first set of data points: (-2, 4) and (4, -8)
- Slope (m) = (y2 - y1) / (x2 - x1) = (-8 - 4) / (4 - -2) = -12 / 6 = -2
- Let's use (4, -8) to find the y-intercept (b)
-8 = -2 * 4 + b
-8 = -8 + b
b = -8 + 8
b = 0
Therefore, the equation relating X and Y is y = -2x + 0 which simplifies to y = -2x.
2. Using the second set of data points: (0, 1) and (3, 10)
- Slope (m) = (y2 - y1) / (x2 - x1) = (10 - 1) / (3 - 0) = 9 / 3 = 3
- Let's use (0, 1) to find the y-intercept (b)
1 = 3 * 0 + b
1 = 0 + b
b = 1 - 0
b = 1
Therefore, the equation relating X and Y is y = 3x + 1.
The two functions that relate the input X and the output Y are:
1. y = -2x
2. y = 3x + 1
To find a function that relates the input X and the output Y, we need to observe the pattern in the given input-output pairs. Once we identify the pattern, we can use it to write a function.
For the first set of input-output pairs:
1. The input values, x, increase by 2 each time: -2, 0, 2, 4.
2. The output values, y, decrease by 4 each time: 4, 0, -4, -8.
Based on this pattern, we can observe that the output y can be obtained by multiplying the input x by -2. Therefore, the function can be written as:
y = -2x.
For the second set of input-output pairs:
1. The input values, x, increase by 1 each time: 0, 1, 2, 3.
2. The output values, y, increase by 3 each time: 1, 4, 7, 10.
Based on this pattern, we can observe that the output y can be obtained by multiplying the input x by 3 and adding 1. Therefore, the function can be written as:
y = 3x + 1.
So, the function for the first set of input-output pairs is y = -2x, and the function for the second set of input-output pairs is y = 3x + 1.