<p>I'm having a problem with functions. Whenever there are f(x)'s or g(x) or f(3)=something in a question I always get stuck. When they use f(3) does it mean subbing in a 3 for the y value? </p>
<p>These questions I don't understand (from BB2, pg 331):</p>
<h1>17. The cost, in dollars, of producing n units of a certain product is given by the function c as c(n)=an+b, where a and b are positive constants. The graph of c is given above. (it is a straight line and is connecting these two points, (0,500) and (12,1100). Which of the following functions, f, represents the average (arithmetic mean) cost per unit, in dollars, when n units are produced?</h1>
<p>a f(n)=50+50/n
b f(n)=50+500/n
c f(n)=500+50n
d f(n)=500+50/n
e f(n)=500+500/n
answer is B</p>
<p>I read the explanation in the book but I still don't understand it.</p>
<h1>18. For all positive values of x, the function f is defined by f(x)=x^3-x^-2. Of the following, which is the best approximation of f(x) for values of x greater than 1000?</h1>
<p>a x^3
b x^4
c x^5
d x^6
e x^9
Answer is A</p>
<p>Help! Functions/whatever are so confusing lol...pleeeaaasseee help meh</p>
<p>Well, I finally worked out how to do 17 and understood it, but I still need help for 18, please!</p>
<p>Just think of a function as something that takes a number (x) and converts it into another number (y). When you see something like y=f(1), it means: shove the number 1 into the function by setting x to 1, and set y to what comes out. Whatever is inside the parentheses is what goes into x.</p>
<p>So, if f(x) = 3x-5, then f(1) = 3(1)-5 = -2. You may see extra stuff inside the parentheses; all of it gets shoved into x. For example, using the same function, f(2-4)=3(-2)-5=-11. An SAT question might read: If f(x) = 3x-5, then for what value of x is f(x) = 22? In this case, you are given y but not x. Since 22 = y = f(x) = 3x-5, then 3x-5 = 22 so x=9. All of this is the same if the letter g or h is used for the function, as in g(x) or h(x).</p>
<h1>18 is less about functions than understanding exponents; you have to know that x^-n = 1/x^n. So, the bigger x gets, the smaller x^-2 gets. But, the the bigger x gets, the larger x^3 gets. So, for big values of x, the function becomes f(x) = x^3 - (really small number). Hope that helps for #18…</h1>
<p>well, my problem about 18 is that I don’t know what it wants me to do…what does it mean by “which is the best approximation of f(x) for values of x greater than 1000?”</p>
<p>Well, here’s one way to think about it: you have this original function – F(x)=x^3-x^-2.</p>
<p>If you asked to apply that function to an x value bigger than 1000 (say 2000 maybe), you would have to find 2000^3 - 2000^-2. But suppose you were willing to settle for an approximate answer? They are asking which one of the choices would be closest.</p>
<p>But how do you know which to pick. You COULD do it the long way – first calculate the exact answer by doing 2000^3- 1/2000^2, and then re-calculate the answer using the function given with each answer choice…</p>
<p>Or you could save a lot of time by noticing that after you calculate 2000^3, the amount you subtracted from it was TINY – small enough to ignore. So f(x) = x^3 is the approximate answer.</p>