Question

Keira created color panels for a wall using a mix of only red and blue paints. She plotted the quantities of red and blue paints used for each mix and connected them using a line segment, as shown in the graph below:

Line graph Color Mix, Quantity of Blue Paint, in mm, on X axis and Quantity of Red Paint, in mm, on Y axis. X axis has a scale from 0 to 9 increments of 1. The Y axis has a scale of 0 to 18 increments of 2. Straight line connecting 3, 2 and 7, 12

Which statement best describes the domain of the function represented in the graph?

3 ≤ x ≤ 12 or x is between 3 and 12, inclusive
3 ≤ x ≤ 7 or x is between 3 and 7, inclusive
2 ≤ x ≤ 12 or x is between 2 and 12, inclusive
2 ≤ x ≤ 7 or x is between 2 and 7, inclusive

Answer 1

"3 ≤ x ≤ 7 or x is between 3 and 7, inclusive" The domain of a function is the range of values for which the function is defined. Since your function is a graph, look at the minimum and maximum values of X for that graph. The graph is a straight line connecting (3,2) to (7,12). So the legal values of X are every value between 3 and 7. And since the value 3 exactly is acceptable as well as the value 7 being acceptable, then the range is from 3 to 7 inclusive. Now look at the available answers and you'll see that "3 ≤ x ≤ 7 or x is between 3 and 7, inclusive" is one of the available choices and it's correct.