The function f(x) represents fewer initial acres than the function g(x): True.
The function f(x) represents more acres harvested per hour than the function g(x): False.
The y-intercept of f(x) is 50 units below the y-intercept of g(x): True.
In Mathematics and Geometry, the y-intercept of any graph such as a linear equation or function, generally occur at the point where the value of "x" is equal to zero (x = 0).
By critically observing the table of values and the function shown in the image below, we can reasonably infer and logically deduce the following y-intercepts:
y-intercept of f(x) for Farmer 1 = (0, 200).
y-intercept of g(x) for Farmer 2 = (0, 250).
Therefore, the function f(x) with an initial acre of 200 units represents fewer initial acres than the function g(x) with an initial acre of 250 units.
For the slope of f(x) and g(x), we have:
Slope of f(x) = -4.
Slope of g(x) = (225 - 250)/(5 - 0)
Slope of g(x) = -5
Therefore, the function f(x) with a slope of -4 does not represent more acres harvested per hour than the function g(x) with a slope of -5.
Difference in y-intercepts = 250 - 200
Difference in y-intercepts = 50 units.
In conclusion, the y-intercept of f(x) is 50 units below the y-intercept of g(x).
Complete Question:
For this item, complete the choice matrix by clicking the appropriate answer in each row. Two farmers use linear functions to represent the total number of acres, f(x) and g(x), remaining to be harvested after x hours.
If 0≤x≤50, determine whether each statement is true or false.
The function f(x) represents fewer initial acres than the function g(x). True False
The function f(x) represents more acres harvested per hour than the function g(x). True False
The y-intercept of f(x) is 50 units below the y-intercept of g(x). True False