{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}


Hence the two functions have the same domain we h f

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (7.5, ∞). We find r(x) < 0 on (7.5, ∞). 1 There is no asymptote at x = 1 since the graph is well behaved near x = 1. According to Theorem 4.1, there must be a hole there. 270 Rational Functions (+) 0 (−) 0 7.5 In the context of the problem, x represents the number of PortaBoy games systems produced and AC (x) is the average cost to produce each system. Solving AC (x) < 100 means we are trying to find how many systems we need to produce so that the average cost is less than $100 per system. Our solution, (7.5, ∞) tells us that we need to produce more than 7.5 systems to achieve this. Since it doesn’t make sense to produce half a system, our final answer is [8, ∞). 4. We can apply Theorem 4.2 to AC (x) and we find y = 80 is a horizontal asymptote to the graph of y = AC (x). To more precisely determine the behavior of AC (x) as x → ∞, we first use long division2 and rewrite AC (x) = 80 + 150 . As x → ∞, 150 → 0+ , which means x x AC (x) ≈ 80 + very small (+). Thus the average cost per system is getting closer to $80 per system. If we set AC (x)...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online