Question

HELP ME PLEASE, AND SHOW THE GRAPHING

Write a function rule that represents the relationship between x and f(x).
Then graph the function rule.
1. Input
X
0
3
6
Output
f(x)
6
9
12

2.
Input
X
0
1
2
Output
f(x)
-3
-2
-1

3.
Input
X
1
2
3
Output
f(x)
4
6
8

Answer 1

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]