Regarding the linear functions in this problem, it is found that:
a. The function is: f(x) = -2.25x + 11.25.
The domain is: x .
b. The function is: g(x) = -2.25x + 15.75.
The graph of g is a translation of the graph of f 2 feet to the right and 4.5 feet up.
What is the linear function?
The slope-intercept representation of a linear function is given as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x increases by one.
b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0.
a) Considering the base and the top of the ladder, the two points are given as follows:
(5, 0) and (0,11.25).
Hence the domain is:
0 ≤ x ≤ 5.
When x = 0, y = 11.25, hence the intercept is of b = 11.25. When x increases by 5, y decays by 11.25, hence the slope is given as follows:
m = -11.25/5
m = -2.25
Thus the function is:
f(x) = -2.25x + 11.25.
B) The translation is defined as follows:
2 units right, as 7 - 5 = 2.
4.5 units up, as 15.75 - 11.25 = 4.50.
When x = 0, y = 15.75, hence the intercept is of b = 15.75.
When x increases by 7, y decays by 15.75, hence the slope is given as follows:
m = -15.75/7
m = -2.25
Thus the function is:
g(x) = -2.25x + 15.75.