Your Algebra Homework Can Now Be Easier Than Ever!

Math 505G Assignments

Properties of Rational Functions

p. 192: 17, 22, 24, 26, 30, 40, 41, 44, 48, 50, 51

17. To figure out the domain of R(x), we must only calculate where x3 − 8 = 0. But now x3 − 8 = 0
x3 = 8 x = 2. Thus our domain is

{x | x ≠ 2}.

22. To figure out the domain of F(x), we must calculate where 3(x2+4x+4) = 0. But now 3(x2+4x+4) =
3(x + 2)2, so our domain is

{x | x ≠ −2}.

24. The graph of this function shows that

(a) Domain = (−∞,−1) ∪ (−1,∞) or {x | x ≠ −1}. Range = (0,∞) or {y | y > 0}.
(b) No x- intercepts and y -intercept (0, 2)
(c) Horizontal asymptote y = 0.
(d) Vertical asymptote x = −1
(e) No Oblique asymptotes

26. The graph of this function shows that

(a) Domain = {x | x ≠ 0} Range = (−∞,−2) ∪ (2,∞) or {y | y < −2 or y > 2}.
(b) No x- or y-intercepts
(c) No horizontal asymptote
(d) Vertical asymptote x = 0
(e) Oblique asymptote y = −x

30. Your graph should look something like :

40. The trick here is noticing that Thus we can graph it using transformations,
getting something that looks like:

41. Let The function is already in lowest terms . Thus the vertical asymptotes are just where
the denominator is equal to zero ,

x = −4.

To find the horizontal asymptotes, first note that our function is not proper. Thus we must perform
long division to obtain

We thus get horizontal asymptote

y = 3

and no oblique asymptotes.

44. Let We can factor this as

Which is already in lowest terms. Thus we find vertical asymptote

x = −5.

To find the horizontal/oblique asymptote, note that the function is not proper, so we must divide.
Long division yields

Which gives us oblique asymptote

y = −x + 5.

There are no horizontal asymptotes.

48. Let Then we can factor this as

Thus our function is in lowest terms, and it follows that our vertical asymptotes are

x = 0, x = −2.

Our function is proper in this case, so we get horizontal asymptote

y = 0.

There are no oblique asymptotes.

50. Let Then we can factor this function as

where the numerator is irreducible (Use the quadratic formula to see this). Thus R(x) is in lowest
terms, and we get vertical asymptotes

The function is not proper, so we must use long division to see that


y = 2

Is the horizontal asymptote, and the function has no oblique asymptotes.

51. Let Then we can write

Our function is not in lowest terms. Thus, to find the vertical asymptotes we must reduce :

It follows that our only vertical asymptote is

x = 0.

Our function is not proper, so to find the horizontal or oblique asymptotes we must use long division
to get

and thus we have oblique asymptote y = −x − 1. There are no horizontal asymptotes.

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 is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for visitors -- if you order Algebra Helper by midnight of February 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 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...)


Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:

OR 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
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.