Final answer:
To find which function the graph represents, we look for the option with a slope of zero, indicating a horizontal line, and consider the behavior of the function within the range of 0 ≤ x ≤ 20. Option B meets the criteria of having a zero slope and fitting the given range, making it the most likely representation of the graph.
Step-by-step explanation:
To determine which function is represented by the graph, we need to understand the characteristics of each option provided and match them with the known properties of the graph described in the question.
Given that the graph of the function f(x) for 0 ≤ x ≤ 20 is a horizontal line, we are looking for a function where the slope b is zero. This is because a horizontal line indicates that there are no changes in the y-value as x increases, implying that the slope of the graph is zero. Referring to Figure 12.4, option B which would indicate a horizontal line if b = 0, meets this criterion.
Moreover, from the information that f(x) is restricted between x = 0 and x = 20, inclusive, we can disregard any functions that would cause the graph to be undefined or to extend beyond this range. This helps us further narrow down the options.
Additionally, based on the scenario provided in question 75, a function with a positive value and a positive slope that is decreasing in magnitude suggests a function that starts with a higher slope and decreases as x increases, such as a quadratic function. Option B, which offers a quadratic equation, could be indicative of such a scenario.
The process of plotting the graph using specific values for (x,y) data pairs can better illustrate the relationship between x and y and confirm our selection of the function that the graph of the function represents.