b Substitute 18 into the equation that you find in Part A.
A
aFunction: c=1200/m-2
Graph:
B
b $ 75
Practice makes perfect
a We are told that the musicians will play a charity benefit and two of them will perform without charge. We have totally $ 1200 to pay them. Now we will write an equation to describe the cost c of hiring one paid musician as a function of the number of musicians m.
c=1200/m-2
Notice that we take the number of musicians as (m-2) because 2 of them will not be paid. Now we want to graph this function. To do so let's recall the general form of a rational function.
y=a/x- h+ k
We need to have the asymptotes of the function to graph it. In this form, the asymptotes are the lines x= h and y= k. Let's now identify the values of h and k for our function.
c =1200/m-2 &⇔ c=1200/m- 2+ 0
We can see that h= 2 and k= 0. Therefore, the asymptotes are the lines x= 2 and y= 0. With this in mind, we will make a table of values to plot the graph easily.
m
1200/m-2
c=1200/m-2
14
1200/14-2
100
26
1200/26-2
50
102
1200/102-2
12
Let's now plot and connect the obtained points with a smooth curve. Since the cost and the number of musicians cannot be negative, we will use only Quadrant I to draw the graph.
b We are asked to find the cost of hiring each paid musician when we use our entire budget to get a total of 18 musicians. To do so we will substitute 18 for m into the equation c= 1200m-2. Let's do it!
