Final answer:
To determine the domain and range of a relationship, we use the given information about intervals and central points. The domain lies between values 65 and 75, which coincides with the x values of the data, while the range is specified with intervals around central points that extend from 0.5 to 5.5.
Step-by-step explanation:
To determine the domain and range for a given relationship, one must recognize which values are allowable for the independent variable (domain) and which values result for the dependent variable (range). Based on the provided boundaries and relations, we can interpret the histogram and equation data to identify these sets.
For the domain, since the values of the independent variable x in the data are between 65 and 75, we can conclude that the domain is 65 ≤ x ≤ 75. Similarly, by analyzing the heights given by intervals, we notice that the possible heights (x values) fall between 59.95 to 75.95, which closely matches the previously identified domain with the addition of small intervals below 65 and above 75.
Regarding the range, it's indicated that the range will be from 0.5 to 1.5 with central points increasing by 1 for each subsequent range up to 5.5. For instance, with central points at 1, 2, 3, 4, and 5, the adjacent intervals extend by 0.5 on either side, resulting in consecutive ranges of 0.5-1.5, 1.5-2.5, and so on.
We can deduce that any graphical representation, such as a histogram, would display the domain on the x-axis and the corresponding frequencies or dependent values as the range on the y-axis. A correctly labeled histogram would demonstrate the intervals and central points as specified, which would help visualize the domain and range more concretely.