Analyze how the profit is changing and think about what the possible values for the inputs of the function can tell you.
See solution.
Practice makes perfect
We are given the graphs shown below relating the profits for selling lemonade. We are asked to determine what situations graphs B, C, and D could represent.
A.
B.
C.
D.
We will discuss each case separately.
Graph B
We can see that the graph is discreet, since it is made out of a finite amount of points. Notice that the profit is increasing until it reaches a point where it stops. This could represent that the first lemonades were sold as normally, and then they started reducing the price of each one. Finally, they ended up giving away the last ones for free.
Graph C
This graph is increasing at a constant rate. This could represent the lemonade being sold at a constant price. However, this is a continuous graph. Therefore, it cannot represent the lemonade being sold by cups, since we can only sell them by integer amounts that way. Nevertheless, we could still model the lemonade sold if it is sold per liter, for example.
Graph D
We can see that the profit shown in the graph is always the same. This could represent that at first the lemonade was sold at a specific price, and the rest of it was given for free. Once more, however, this could only model lemonade sold if it is sold per liter, for example. Selling it by cups forces us to use a discreet graph, as we discussed before.
