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Math 380 Exam 2

Work out the following problems on scratch paper. Do not write your answers on these
sheets. Number each problem clearly and show work when possible. At the end, staple
just your worksheets and turn them in with your name on the first page. You may keep
this test. If you have any questions, please ask. Good luck!

1. (3 pts each) Suppose that f(x) = -3x2 + 4. Find the following and simplify where
possible:

a) f(1)
b) f(-1)
c) f(a)

2. (4 pts each) Find the domain and range of each of the following. You may use either
set-builder or interval notation. Assume each box is worth 1. Assume the graphs
continue indefinitely at their ends.

For 3-6, when solving algebraically : Make your steps clear . If using substitution, show
which equation you solved for which variable ; if using elimination, show clearly which
equation you multiplied by what number . If you get no solution or the same line, show
the final equation! You must express your solutions in set -builder notation if your
equations turn out to be the same line!

3. (10 pts) Consider the system of equations :

x - y = 7
3x - 5y = 15

a) Graph each line carefully on graph paper. Make sure the intersection (if
there is one) is clear on your paper. What is the solution(s)? If the lines are
the same
, write the solution set in set-builder notation.

b) Now solve the system algebraically . You may use either substitution or
elimination
method.

4. (10 pts) Consider the system of equations:

3x + 2y = 2
-2x + y = 8

a) Graph each line carefully on graph paper. What is the solution(s)? If the
lines are the same, write the solution set in set-builder notation.

b) Now solve the system algebraically. You may use either substitution or
elimination method . Do NOT just CHECK your guess from part a)!

5. (10 pts) Consider the equation .

(a) Setting   and y2 = −x + 2 , carefully graph both lines on graph
paper, labeling which is which. Make sure your graph shows the
intersection point. If necessary, adjust the scale so each box counts for
more than 1. Looking at your graph, estimate the solution to the equation.
Write this near the intersection on your graph.

(b) Now solve the equation algebraically. Was your estimate close? Do NOT
just CHECK your guess from part c)!

6. (10 pts) A chemist is working on a flu vaccine. She needs to mix a 10% sodium-iodine
solution with a 60% sodium-iodine solution to obtain 50 milliliters (mL) of a 30%
solution. How many mL of 10% and 60% should be used? Set up a system of
equations and solve.

7. (3 pts each) Simplify the following exponent problems as much as possible,
eliminating all negative exponents . Multiply out powers of constants (write 22 as
4, for example). If it cannot be simplified, state “cannot be simplified.”

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