In this discussion, you are assigned two rational expressions to work on.
Remember to factor all polynomials completely. Read the following instructions
in order and view the example (available for download in your
online classroom) to complete this discussion. Please find the two rational
expressions assigned to you in the table below. First Rational Expression: 1 – x2 xSecond Rational Expression: 2b – 2 2b2 – 8 Explain in your own words what the meaning of domain is. Also, explain why a
denominator cannot be zero.
Find the domain for each of your two rational expressions.
Write the domain of each rational expression in set notation (as
demonstrated in the example).
Do both of your rational expressions have excluded values in their domains?
If yes, explain why they are to be excluded from the domains. If no, explain why
no exclusions are necessary.
Incorporate the following five math vocabulary words into your discussion.
Use bold font to emphasize the words in your writing. Do not
write definitions for the words; use them appropriately in sentences describing
your math work.
Domain
Excluded value
Set
Factor
Real numbers
Your initial post should be at least 250 words in length. Support your claims
with examples from required material(s) and/or other scholarly resources, and
properly cite any references.**SEE ATTACHED EXAMPLE TO KNOW HOW TO FORMAT THE ANSWER*****ALSO, I MAY HAVE QUESTIONS AFTER I CONFIRM PAYMENT, I WOULD LIKE TO HAVE SOMEONE WHO WILL BE WILLING TO ANSWER ME, AND HELP ME UNDERSTAND THE ANSWER BETTER, EVEN THOUGH HE/SHE HAS BEEN PAID***mat222.w1.discussionexample.pdfINSTRUCTOR GUIDANCE EXAMPLE: Week One Discussion
Domains of Rational Expressions
Students, you are perfectly welcome to format your math work just as I have done in
these examples. However, the written parts of the assignment MUST be done about
your own thoughts and in your own words. You are NOT to simply copy this wording
into your posts!
Here are my given rational expressions oh which to base my work.
25×2 – 4
5 – 9w
67
9w2 – 4
The domain of a rational expression is the set of all numbers which are allowed to
substitute for the variable in the expression. It is possible that some numbers will not be
allowed depending on what the denominator has in it.
In our Real Number System division by zero cannot be done. There is no number (or
any other object) which can be the answer to division by zero so we must simply call the
attempt “undefined.” A denominator cannot be zero because in a rational number or
expression the denominator divides the numerator.
In my first expression, the denominator is a constant term, meaning there is no variable
present. Since it is impossible for 67 to equal zero, there are no excluded values for the
domain. We can say the domain (D) is the set of all Real Numbers, written in set
notation that would look like this:
D = {x| x ∈ ℜ} or even more simply as D = ℜ.
For my second expression, I need to set the denominator equal to zero to find my
excluded values for w.
9w2 – 4 = 0
(3w – 2)(3w + 2) = 0
3w – 2 = 0 or 3w + 2 = 0
3w = 2
or 3w = -2
w = 2/3 or w = -2/3
I notice this is a difference of squares which I can factor.
Set each factor equal to zero.
Add or subtract 2 from both sides.
Divide both sides by 3.
These are the excluded values for my second expression.
The domain (D) for my second expression is the set of all Reals excluding ±2/3. In set
notation, this can be written as D = {w| w ∈ ℜ, w ≠ ±2/3}
Now, both of my expressions do not have excluded values. In one expression, I have no
excluded values because there is no variable in the denominator and a non-zero number
will never just become zero. In the other expression, there are two excluded numbers
because both, if inserted in place of the variable, would cause the denominator to become
zero and thus the whole expression would become undefined.
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