Answer:
Explanation:
To find the function rule for the relationship between x and f(x), we can perform a linear regression analysis on the given data points. This can be done using a spreadsheet software or a statistical software. One way to do this is to use the equation of a straight line, which is y = mx + b, where y is the output (f(x)), x is the input, m is the slope, and b is the y-intercept.
The slope m can be calculated as:
m = (Δy / Δx) = (f(x2) - f(x1)) / (x2 - x1) = (9 - 6) / (3 - 0) = 3
The y-intercept b can be calculated as:
b = f(x) - mx = 6 - 3x
So the function rule is:
f(x) = 3x + 6
To graph the function, we can plot the given data points and then draw a straight line that passes through those points. The graph of the function should look like this:
[!graph of f(x) = 3x + 6]
The function rule for the relationship between x and f(x) can be found using a similar process. Using the given data points, we can calculate the slope and y-intercept:
m = (Δy / Δx) = (f(x2) - f(x1)) / (x2 - x1) = (-2 - (-3)) / (1 - 0) = 1
b = f(x) - mx = -3 - x
So the function rule is:
f(x) = x - 3
The graph of the function should look like this:
[!graph of f(x) = x - 3]
For the third example, we can find the function rule using a similar process:
m = (Δy / Δx) = (f(x2) - f(x1)) / (x2 - x1) = (6 - 4) / (2 - 1) = 2
b = f(x) - mx = 4 - 2x
So the function rule is:
f(x) = 2x + 4
The graph of the function should look like this:
[!graph of f(x) = 2x + 4]