answer in a detailed manner please Find the domain and the range of the function

Question

answer in a detailed manner please

Find the domain and the range of the function below. F(x) = x5+x1/2 Find the linear equation that has points below and plot the equation. (0,-1), (-5,3) Assume that a company's revenue and cost functions are given below, where R(x) represents the revenue in dollars, C(x) represents the cost in dollars, and x represents the number of products produced. Find the break-even point. R(x) = 78x C(x) = 13200 + 43x Plot f(x) and g(x) below. Explain the transformations from f(x) to g(x). f(x) = cos x g(x) = -2cos(x/3)

Explanation / Answer

1. Domain is x>=0

Range is y>=0

2. To get the slope we use

(y2-y1)/(x2-x1)=(-5-0)/(3-(-1))=-1.25

Then we plug that into the equation y=mx+b where m is slope and b is y intercept, which is known because one of the points given is the y intercept. Thus we get:

y=1.25x-1

3. We want to find the point of intersection of these two graphs by setting them equal to eachother.

78x=43x+13200

78x-43x=13200

35x=13200

Divide by 35

x=377.14

Because there is no such thing as .14 of a product, we must round up to 378. So that means that at 378 products, the company will have broken even. If you need to know the amound of money that represents, you multiply 377.14*78 because in the first function, that will give us f(x) or the y value.

4. This is the graph of cos(x): http://www.wolframalpha.com/share/clip?f=d41d8cd98f00b204e9800998ecf8427e42uprhtje

and this is the graph of -2cos(x/3):http://www.wolframalpha.com/share/clip?f=d41d8cd98f00b204e9800998ecf8427e740ml234rh

as you can see, not only has the graph been flipped over the x axis but it has also had it's amplitude increased from 1 to 2. The period has also increased from 2pi to 6pi

Any questions just ask :)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.