State the domain and range and explain the importance of the horizontal asymptote in the following case:The profit, in thousands of dollars, from...

The function for the profit is given as:
P(x)=(5x-400)/(x+600)

Note:
Here, the domain is x > 0. I have taken this as the domain under the assumption
that you cannot sell less than 0 kilograms of tuna and for x = 0 the function is not
defined. The range for the domain x> 0 is
y<=5.

f(x) = (5x - 400)/ (x +
600)

The horizontal asymptote is f(x) =
5.

We get a horizontal asymptote as even if x-->
inf, the value of the function can grow till only 5. So, even if a very large number of
tuna is sold the maximum profit is only 5.

The required
domain is x>=0 , range is
y<=5. The horizontal asymptote places a limit on the
maximum profit.