Question

Please help I don’t understand number 16

Answer 1

Let's go step by step:

a) You are given four couples of x and y values which model the relationship between the number of drinks and their cost. So, the couple $(x,y)=(0,0)$ means that if you buy zero drinks, you spend no money. That makes sense. The next information we have is $(x,y) = (2,3)$, which means that two drinks cost 3 dollars, and so on.

So, you simply need to draw on the grid the four points

$(0,0),\ (2,3),\ (4,6),\ (6,9)$

b) The domain is the set of inputs. Since we only know the value of the function on four different points (we know the price for 0,2,4 and 6 drinks), the domain is discrete. In fact, a continuous domain must contain an interval (for example, $[1,2]$ is a continuous domain), whereas if you pick a certain number of points (like in this case: we picked 0,2,4 and 6), the domain is discrete.

c) Once the points are drawn on the grid, you can see that they all lie on the same line. To find that line, we will only need two of those points (once two points are fixed, there is only one line passing through them). In general, the equation of the line passing through $P = (P_x,P_y)$ and $Q = (Q_x,Q_y)$ is

$\cfrac{x-P_x}{Q_x-P_x} = \cfrac{y-P_y}{Q_y-P_y}$

Let's choose, for example, the first two points. The equation is

$\cfrac{x-0}{2-0} = \cfrac{y-0}{3-0} \iff \cfrac{x}{2} = \cfrac{y}{3} \iff y=\cfrac{3}{2}x$

d) Now that we know the equation of the line, we can compute the cost of any number of drinks: the equation of the line is a function that associates a cost, y, with every possible number of drinks, x.

Of course, some associations will be odd - we can compute the cost of $\sqrt{2}$ drink, but what would it mean?

Anyway, the question about the cost of two drinks seems more than reasonable, so let's see which y value is associate with the particular x value of 2:

$y = \cfrac{3}{2} x \implies y = \cfrac{3}{2}\cdot 2 = 3$

So, two drinks cost 3 dollars.