What is the function rule when the input is 0,1.2.3 and the output is 5,4,3,2?
x: 0 1 2 3
y: 5 4 3 2
to get the function, we choose two points. let's just choose the first two points,, that is, point1 (0,5) and point2 (1,4)
now, we get first the slope. the slope is given by the equation,
slope = m = (y2 - y1)/(x2 - x1)
where
y1 = y-coordinate of point1
x1 = x-coordinate of point1
y2 = y-coordinate of point2
x2 = x-coordinate of point2
for point1=(0,5) and point2=(1,4)
y1 = 5 , x1 = 0 , y2 = 4 and x2 = 1
substituting,
m = (y2 - y1)/(x2 - x1) = (4-5)/(1-0) = -1/1 = -1
then we substitute it in the slope-intercept form equation:
y - y1 = m(x - x1)
substituting with y1 = 5, x1 = 0 and m = -1,
y - 5 = -1(x - 0)
y - 5 = -x
x + y - 5 = 0
x + y = 5
hope this helps~ :)
To determine the function rule, we can examine the pattern between the input and output values:
Input (x) : 0, 1, 2, 3
Output (y) : 5, 4, 3, 2
From the input to the output, it can be observed that for every increase in the input by 1, the output decreases by 1.
Therefore, the function rule in this case is likely to be a linear function with a constant rate of change (-1).
The equation representing the function rule can be written in the form:
y = mx + b,
where:
m represents the slope (rate of change)
b represents the y-intercept (the value of y when x = 0).
Using the data provided, we can calculate the slope (m) as follows:
m = (change in y) / (change in x)
m = (5 - 4) / (0 - 1)
m = 1 / (-1)
m = -1
Since we know the slope (m), we can find the y-intercept (b) by substituting one of the given points into the equation and solving for b. Let's use the point (0, 5):
5 = (-1)(0) + b
5 = b
Therefore, the function rule is:
y = -x + 5.
To find the function rule when given a set of input-output pairs, we need to identify the relationship between the input and output values. In this case, we are given the inputs 0, 1, 2, and 3, and their corresponding outputs are 5, 4, 3, and 2 respectively.
One approach to find the function rule is to look for a pattern or observe any consistent change between the input and output values. Let's analyze the given data:
When the input value increases by 1, the output value decreases by 1. This means there is a linear relationship between the input and output.
To express this relationship mathematically, we can use the equation y = mx + b, where y is the output, x is the input, m is the slope, and b is the y-intercept.
In this case, since each time the input increases by 1, the output decreases by 1, we can deduce that the slope (m) is -1.
Now, to find the y-intercept (b), we can substitute the values for one of the input-output pairs into the equation.
Let's use the pair (0, 5):
5 = -1(0) + b
5 = b
Therefore, the y-intercept (b) is 5.
Our function rule is y = -x + 5.
Now, we can use this function rule to find the output for any given input value.