The linear functions in this problem are given as follows:
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
For function f(x), when x increases from 2 to 3, f(x) decays from 5 to 1, hence the slope is of -4 and:
f(x) = -4x + b.
When x = 2, f(x) = 5, hence the y-intercept is found as follows:
5 = -4(2) + b
b = 13.
Then:
f(x) = -4x + 13.
For function g(x), when x increases from 4 to 7, g(x) increases from 2 to 8, hence the slope is of:
m = (8 - 2)/(7 - 4) = 6/3 = 2.
Hence:
g(x) = 2x + b.
When x = 4, g(x) = 2, hence the y-intercept is found as follows:
2 = 2(4) + b
2 = 8 + b
b = -6.
Then:
g(x) = 2x - 6.
More can be learned about linear functions at brainly.com/question/24808124
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