Could someone help me with these questions? Thank you. 1. The horizontal asympto
ID: 3091601 • Letter: C
Question
Could someone help me with these questions? Thank you.1. The horizontal asymptote of the function f(x)=4x^3+5x/(2x^3+7)
--> I think it is y=2.
2. The graph of y-7= (x+2)^2 can be obtained from the graph ofy=x^2 by shifting the graph 7 units above and 2 units left. (I saidthis was true)
3. Which of the following is true about the graph of y= x^3+8
a)x intercept is -2,0
b) y-intercept is 0.8
4. Which of the following is true about the function y=5+2x-3x^2
a) minimum at vertex
b) maximum at the vertex
5. Given that the total-cost function (in dollars) for producingwidgets is
C(x) = 25x + 27500, what would you expect each widget to cost(excluding setup
costs)?
(a) $25
(b) $27500
(c) $27525
Explanation / Answer
1. Correct. y = 2 since the leading terms are the same you justtake the coefficients. 2. Right, true. y = (x+2)^2 + 7 indicates moving 7 units up and youdo opposite sign of whatever is in the parentheses for left/rightmovement. 3. x-intercept means et y = 0 and solve for x. x3 + 8 = 0 x3 = -8 x = -2 so (-2,0) is the x-intercept. y-intercept means plug in x = 0 ---> y =03 + 8 = 8 ---> y-intercept is (0, 8) 4. Look at the coefficient of the x2 term. If it'spositive, the vertex is a min. If it's negative the vertex is amax. Here it's negative so a max occurs at thevertex. 5. total cost = variable cost + fixed cost The fixed cost is the setup cost. variable cost = (price of widgets)(quantity ofwidgets) So each widget is $25.