Question

The number of large and small iron-on transfer designs you can apply to T-shirts in 16 minutes is represented by the equation 4x+2y=16. The table shows the number of large and small designs. The graph provided shows the large designs, x, and the small designs, y. PART A. Find the domain and range of the function represented by the table.PART B. Explain what the domain is, in context of this problem. PART C. Why is x=5 not in the domain of the function represented by the table?

Answer 1

Part A

The domain of a function is the set of possible values for the independent variable x, we can express the domain in interval notation like this: [xmin, xmax] where "xmin" is the minimum value of x and "xmax" is the maximum value of x. In this case, x goes from 0 to 4, then the domain of this function is [0, 4], the range is also the set of possible values but for the dependent variable y, then it can be represented like this: [ymin, ymax], in this case, "ymin" equals 0 (the smaller possible value of x according to the table) and "ymax" equals 8, then the range of the function is [0, 8].

Part B

As mentioned, the domain represents the set of possible values for x, in this context, x is the number of large designs that you can apply to T-shirts, then the domain is the set of possible large designs that can be applied, any number out of this interval ([0, 4]) can't be included like x=5.

Part C

As you can see, we have a linear relationship between x and y, as x increases, y decreases, once that we have reached the value of 4 of large designs we have a corresponding 0 for the number of small designs, then you can't jump up to x=5 because you would have a negative value for the variable "y".