# 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) = -3x^{2} + 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 y_{2} = −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 2^{2}
as

4, for example). If it cannot be simplified , state “cannot be simplified.”

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