Quiz 3

Date: MATH 1090-4 - Fall 2003

Note: Unless stated otherwise, answers without justification receive no credit. Please, show your work!

1. The graph of $f(x)=2x-x^2$ is shown in Figure 1.

   Figure 1: Graph of $f$ for exercise 1

   
   1. What are the coordinates of the point $Q$?
   2. What are the $x$-coordinates of the points on the graph whose $y$-coordinates are 0?
   3. If the coordinates of the point $P$ on the graph are $(a,b)$, how are $a$ and $b$ related?

2. Let $A(x) = x^2$ and $B(x) = 2x-1$. Find:
   1. $(A-B)(x)$.
   2. $(A\circ B)(x)$.
   3. $(B\circ A)(x)$.

3. What is the domain of $f(x) = \sqrt{x+1}$?

4. A museum's entrance ticket costs $ 10 for each person. They also offer a discounted price for groups of, at least, 9 people. For each person above the number 8, the price of each ticket is reduced by 10 cents.

   For instance, for 9 people each ticket costs $ 9.9 and the total price is $9\times 9.9 = 89.1$.

   If $n$ is the number of people in excess of 8 in a group, express the total price for the group as a function of $n$ (assume $n\geq 0$).