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: A line graph titled Color Mix, with Quantity of Blue Paint, in millimeters, on the X axis and Quantity of Red Paint, in millimeters, on the Y axis. The X axis has a scale from 0 to 9 with an increment of 1. The Y axis has a scale of 0 to 18 in increments of 2. A straight line connecting 3, 2 and 7, 12 is drawn. 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

Explanation:

First, you plot the two points (3,2) and (7,12).

Then, you scale the x-axis from 0 to 9 with increments of 1, and 0 to 18 for the y-axis with increments of 2.

Finally, you extend the line by connecting the two dots and extending both sides.

Answer 2

The first thing I did was follow all the instructions using MS Excel as a tools. First I plot the two points (3,2) and (7,12). Then, I scaled the x-axis from 0 to 9 with increments of 1, and 0 to 18 for the y-axis with increments of 2. Finally, I extended the line by connecting the two dots and extending both sides. The result is shown in the picture.

So, from the scale of the axes alone, the domain of the function is the coverage of all its x-values. If the line has coordinates on that x-value, it is part of the domain. Basing on the picture the domain is 2.2≤x≤9. So, the lower limit must not be lower than 2, and the upper limit must not be greater than 9. Among the choices, the accepted values that are still part of the domain is 3 ≤ x ≤ 7.