Answer:
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: Vertical asymptotes is x = 0 and the horizontal asymptotes is y = 12.
The average cost approaches to 12 when the number of shirts increases.
Step-by-step 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:
[tex]f(x)=\dfrac{100+12x}{x}[/tex]
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
[tex]x=0[/tex]
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,
[tex]\dfrac{\text{ Leading coefficient of numerator}}{\text{ Leading coefficient of denominator}}\\\\=\dfrac{12}{1}\\\\=12[/tex]
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
[tex]\lim_{x\to \infty}\dfrac{100+12x}{x}=12[/tex]
Hence, the average cost approaches to 12 when the number of shirts increases.
