Identify the domain and range of the function below. Domain Range
1 answer:
You might be interested in
Answer:
(a) P(x) = 300 x - 3600
(b) P(340) = $ 98400
(c) At least 12 items must be sold to avoid losing money.
Step-by-step explanation:
Part (a):
The Profit function is the difference between the revenue function (R(x)) and the Cost (C(x)) function:
P(x) = R(x) - C(x)
P(x) = 384 x - [84 x + 3600]
P(x) = 384 x - 84 x - 3600
P(x) = 300 x - 3600
Part (b):
The profit on 340 items is:
P(340) = 300 (340) - 3600
P(340) = 102000 - 3600
P(340) = $ 98400
Part (c):
To avoid losing money, the profit P(x) has to be larger or equal than zero. That is:
P(x) 0
300 x -3600 0
300 x 3600
x 3600/300
x 12
So at least 12 items must be sold to avoid losing money.
<h3>Answer: -2</h3>
======================================================
Work Shown:
-------------------
Explanation:
In the second step, I multiplied top and bottom by 1/x. This divides every term by x. Doing this leaves us with various inner fractions that have the variable in the denominator. Those inner fractions approach 0 as x approaches infinity.
I'm using the rule that
where k is some positive real number constant.
Using that rule will simplify the expression greatly to leave us with -2/1 or simply -2 as the answer.
In a sense, the leading terms of the numerator and denominator are -2x and x respectively. They are the largest terms for each, so to speak. As x gets larger, the influence that -2x and x have will greatly diminish the influence of the other terms.
This effectively means,
I recommend making a table of values to see what's going on. Or you can graph the given function to see that it slowly approaches y = -2. Keep in mind that it won't actually reach y = -2 itself.