Final answer:
A horizontal line graph for a linear function where f(x) is constant at 20 is represented by the function rule f(x) = 20. For a loan officer reaching 95 percent of their goal, the function is f(x) = 0.95x. When graphing, the x and y axes are scaled to the maximum values, and in this case, the line is horizontal at y = 10 from x = 0 to x = 20.
Step-by-step explanation:
To write the rule for a linear function like f(x), we need to understand the properties of its graph. A horizontal line represents a function where the value of f(x) stays constant, no matter what x-value we input, as long as it is within the domain of the function. If the graph is a horizontal line at y = 20, the function rule is f(x) = 20. This is because the y-value does not change with x, and hence the slope (m) is 0, reflecting no change in y for any change in x. For the domain 0 ≤ x ≤ 20, f(x) will be 20 for all x in that range.
If a loan officer makes 95 percent of the goal, the linear function representing this scenario can be written as f(x) = 0.95x, assuming x represents the total goal amount. The y-intercept in this case would be 0, as the officer earns nothing if no goal is met (x=0), and the slope of this function is 0.95, which signifies the rate at which the officer's earnings increase with respect to the goal.
When graphing f(x) = 10 with the domain of 0 ≤ x ≤ 20, we label the graph with f(x) and x, and scale the axes to accommodate the maximum values in both dimensions. Since the function is constant at 10, the line would be drawn horizontally across the y-axis at y = 10, from x = 0 to x = 20.