Hi Jeff N.,
Let's take these problems a stage at a time; that way, you can learn how to do the same!
For problem 1. The current price structure is (where C(n) is the total cost for n prints)
So, they plan to raise the cost per print by $0.10. That is per print, which means the total cost increases by 0.10*(the number of prints), or 0.10n. That would then look like:
C(n) = 0.50n if 0<=n<=10
0.40n if n>10
Do you see that the conditions for n did not change, only the prices? Since the cost increase was across the board.
Then, apply the 25% discount for n>50. SInce this applies within (a portion of) the region of n>10, that will then be a total cost of 0.30n (= 0.40n * 75%). OK?
So finally, write this as the multi-domain function:
C(n) = 0.50n if 0<=n<=10
= 0.40n if 10<n<=50
=0.30n if n>50
that would be answer (C), obviously. The other choices were in there to make sure that you didn't misapply the regions for n, or miscalculate a 25% discount. You wouldn't do that, would you??
For question 2, you need to think first about what kind of graphs each of the functions listed in the definition has. For the first one, f(x)=x^2 + 2, you should know by now that that will be a parabola, concave upwards, centered at x=0, with a y-intercept there of 2. How should you know that? 1. Parabola: has an x^2 term in the expression! 2. Concave upwards: the sign on the x^2 term is positive. 3. Centered at x=0: there are NO x^1 terms in the expression; if there were, the parabola would be centered at some different x value -- does the phrase "completing the square" mean anything to you? That's how you might figure out where the parabola is centered. "Centered" means here, that it reflects right-left across that x-value line. If your expression is written in the form f(x)= ax^2 + bx + c , then the parabola is centered at (-b/2a), by the way.
And lastly 4. with a y-intercept there of 2, because if you substitute x=0 into x^2 + 2, you end up with 2 as the answer, and that is f(x) which is a y-value. OK so far?
So your choice is now between (B) or (D), these two have parabolas for x<4. So next, substitute in x=4, and check the result: x^2 + 2 = 18. The scale for answer (B) is way off, but the scale for (D) is correct. So the answer is (D).
So Jeff N., if you have scanned my text here just=only for the right answers, so that you can copy them, you have not done yourself (or me) any favors. You need to slow down, and think a bit at a time about the meaning of the words and equations in math word problems. This is not impossible stuff, it is just a particular way about thinking about the world around you -- the math way, you might call it. Like any language (por favor!), it can be learned, because you have a brain with a lot of reserve capacity.
As proof, I might ask, how many languages can you count 1-10 in? It's 1. fun, 2. it's incredibly useful if you travel, and 3. it's a great ice-breaker at nerdy parties! And if you can think of 8 more reasons, then maybe you'll have to go back and start learning 11 in all those languages, too.
-- Cheers, --Mr. d.