The completed statement can be presented as follows;
The function g(x) has the greatest y-intercept. Its y-intercept is 5
The function f(x) has the greatest x-intercept. Its x-intercept is 3/4
The function f(x) has the greatest rate of change. Its rate of change is 4
The steps used to complete the sentence can be presented as follows;
The function f(x) is; f(x) = 4·x - 3
The slope of the function g is; (11 - 1)/(3 - (-2)) = 2
The equation of function g is therefore; y - 1 = 2·(x - (-2))
y = 2·x + 4 + 1
Therefore; g(x) = 2·x + 5
The above equation for function g has a slope of 2 and a y-intercept of 5
Therefore, function g has the greatest y-intercept, its y-intercept is 5
The x-intercept of function f is; f(x) = 0, therefore; 4·x - 3 = 0
x = 3/4
The x-intercept of function f is 3/4
The x-intercept of function g is; g(x) = 0, therefore; 2·x + 5 = 0
x = -5/2
The x-intercept of function g is -5/2
Function f has the greatest x-intercept. Its x-intercept is 3/4
The slope, which is the rate of change of the function f is 4, while the slope which is the rate of change of the function g is 2. Therefore, function f has the greatest rate of change. Its rate of change is 4