Your Algebra Homework Can Now Be Easier Than Ever!

College Algebra 1110-005: Test #3

Welcome to the third College Algebra test! Your weapons of choice are a pen or pencil,
this test, and your brains. You are not al lowed to use any books, notes (except the provided
crib sheet), or calculators . Some general hints to help you maximize your points:

1. Show as much work as you can, since doing so gives me more opportunities to award
you with partial credit.

2. Don’t spend time converting your solutions to decimal notation — it’s perfectly acceptable
(in fact, it’ s preferred !) to write 1/3 instead of 0.333 . . . or ln(2) instead of
0.693 . . ..

3. By the same token, don’t spend too much time expanding polynomials. As a rule of
thumb, it’s perfectly acceptable to leave any polynomial with a degree higher than two
in factored form.

4. Be sure to read each question carefully! Failure to do so will result in a significant loss
of points, even if the answer you arrive at is correct.

5. If you have any questions during the test, don’t hesitate to ask me! If a problem is
unclear to you, it is probably unclear to your classmates as well.

Good luck, and may the Force be with you!

True & False

1. Mark the following statements as either true or false. If the statement is false, provide
a counter-example or justification.

(a) (2 points) Every polynomial of degree n has n factors (not all of which may be
distinct) over the complex numbers

(b) (2 points) If the complex number a + is a factor of the polynomial p(x), then so
is a −.

(c) (2 points) Every one-to- one function has an inverse.

(d) (2 points) Every exponential function of the form f(x) = ax, with a > 0, is a
strictly increasing function.

(e) (2 points) If ax = ay, then x = y.

(f) (2 points) The inverse of a logarithmic function is an exponential function.

Algebraic Manipulation

2. Solve each equation for x . Be sure to simplify your answer as far as possible, and convert
any logarithms in your final results to the natural logarithm (“ln”) if applicable.

Short Answer

3. (8 points) Factor the polynomial using long division and the Rational
Zeros Theorem . (Hint: The Rational Zeros Theorem states that a polynomial of the
form can only have rational zeros of the form p/q, where p
is a factor of a0 and q is a factor of an.)

4. (8 points) Write a fifth degree polynomial with real coefficients that has the roots r 1 = 0,

5. (8 points) Let

What is f1(x)?

Analysis

6. Consider the exponential function f(x) = 22-x+ 1.
(a) (4 points) Draw a graph of f (x) in the space provided.

(b) (6 points) What is the domain of f(x)?

(c) (6 points) What is the range of f(x)?

(d) (4 points) What is f(0)?

(e) (4 points) For what value(s) of x does f(x) = 2?

Applications

7. Consider the case of continuously compounding interest .
(a) (8 points) For fixed principle P, interest rate r, and compounding period n, how
long will it take double your investment? (Hint: Your annuity is 2P in this case.
Solve for t.)

(b) (8 points) For fixed principle P, compounding period n, and time t, what interest
rate is required to double your investment? (Hint: Your annuity is again 2P, but
this time you must solve for r.)

See You Space Cowboys. . .

Prev Next

Start solving your Algebra Problems in next 5 minutes!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of July 21st you will pay only $39.99 instead of our regular price of $74.99 -- this is $35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:



Algebra Helper can solve problems in all the following areas:

  • simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
  • factoring and expanding expressions
  • finding LCM and GCF
  • (simplifying, rationalizing complex denominators...)
  • solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
  • solving a system of two and three linear equations (including Cramer's rule)
  • graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
  • graphing general functions
  • operations with functions (composition, inverse, range, domain...)
  • simplifying logarithms
  • basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
  • arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath
Check out our demo!
 
"It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..."
C. Sievert, KY
 
 
Sofmath
19179 Blanco #105-234
San Antonio, TX 78258
Phone: (512) 788-5675
Fax: (512) 519-1805
 

Home   : :   Features   : :   Demo   : :   FAQ   : :   Order

Copyright © 2004-2018, Algebra-Answer.Com.  All rights reserved.