Question

The school band is selling t-shirts for a fundraiser. The initial cost for a steamer to apply the decals is $100. It is predicted that the cost of material for each shirt is $12. The function that shows the band’s average cost per t-shirt after x t-shirts are sold is:

f(x)=100+12x/x
complete the following statements;

the vertical asymptotes is x= ANSWER=0
the horizontal asymptotes is y= ANSWER=12

the average cost ot make a tshirt apporaches __$ as the number of tshirts increases ANSWER: 12

Answer 1

The vertical asymptote is x = 0

The horizontal asymptote is y = 12

The average cost to make a t-shirt approaches $12 as the number of t-shirts made increases.

Answer 2

Answer: Vertical asymptotes is x = 0 and the horizontal asymptotes is y = 12.

The average cost approaches to 12 when the number of shirts increases.

Explanation:

Since we have given that

Initial cost for a steamer to apply the declas = $100

Cost of material for each shirt = $12

Function representing the band's average cost per t-shirt after x t-shirt are sold is given by:

`f(x)=(100+12x)/(x)`

We need to find the vertical asymptotes , horizontal asymptotes and the average cost to make a t-shirt approaches as the number of t-shirts increases,

For vertical asymptotes , we will make denominator equal to zero.

So, it will be

`x=0`

Thus, vertical asymptotes is x= 0.

Similarly,

For horizontal asymptotes, we first check the degree of both numerator and denominator.

Since we can see that both have the same degree i.e. 1.

So,

`\frac{\text{ Leading coefficient of numerator}}{\text{ Leading coefficient of denominator}}\\\\=(12)/(1)\\\\=12`

So, the horizontal asymptotes is y = 12.

When the number of shirts increases ,The average cost to make a T-shirt approaches is given by

`\lim_(x\to \infty)(100+12x)/(x)=12`

Hence, the average cost approaches to 12 when the number of shirts increases.