Description
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 to complete this discussion. Please complete the following problems according to your assigned number. (Instructors will assign each student their number.)
My number is 35
If your assigned number is: | Your first rational expression is | Your second rational expression is |
1 | a2 + 2a – 10 | 2x – 8 |
2 | y2 + 11y + 30 | 5a – 3 |
3 | u2 + u – 72 | 2w – 1 |
4 | x2 – 6x – 55 | b – 3 |
5 | 16b2 – 1 | c2 + 2c – 10 |
6 | 4w2 – 9 | y2 – 4 |
7 | a2 + 6a + 9 | t2 + 2t – 10 |
8 | 81m2 – 16 | 22x + 11 |
9 | 3a2 + 16a + 5 | b2 + 7b + 10 |
10 | 4x2 – 1 | r2 + 2r – 24 |
11 | t2 – 14t + 49 | 3q2 – 22q + 24 |
12 | v2 – v – 20 | 6t – 3 |
13 | n2 – 2n – 15 | 8k + 6 |
14 | 64k2 – 9 | s2 + 2s – 15 |
15 | 4k2 – 12k + 9 | 3w2 + 36 |
16 | 5m2 + m | 12a – 15 |
17 | 7t2 – 14t | 36 – w2 |
18 | 22x + 11 | 1 – 2c |
19 | 20c3 + 5c2 – c | 3a2 – 12a |
20 | g2 – 36 | 7n – 2 |
21 | 1 – 2x + x2 | 2c2 + 5c – 25 |
22 | 144 – w2 | z2 – 8z + 16 |
23 | 4 + 16n2 | 3x2 – 2x – 1 |
24 | y2 – 25 | 37 |
25 | a2 – 100 | 3b2 – 9 |
26 | 1 – x2 | 2u – 2 |
27 | 3z + 3 | 5y3 – 75y |
28 | 9 – 36x2 | 15k2 – 5k |
29 | x2 – 7x + 12 | w2 – 9w – 36 |
30 | m2 + 13m + 40 | 4y – 3 |
31 | k2 – 8k | 2b + 1 |
32 | 9b2 + 3 | 2x – 6 |
33 | 15x2 + 45 | 42 |
34 | g2 + 46g | 3k + 1 |
35 | 4a – 5 | 4m3 +16m |
36 | x2 – 25 | b2 – 18b + 81 |
37 | 9m2 – 4 | 5x + 15 |
38 | d2 + 9 | m2 + 4m – 5 |
39 | 13n2 – 13n | 2w + 1 |
40 | 4x3 – 16 | 14 |
41 | x2 + 2x – 10 | 2x – 8 |
42 | x2 + x – 72 | 5b – 3 |
43 | w2 + 11w + 30 | 2n – 1 |
44 | g2 – 6g – 55 | k3 + k |
45 | 16t2 – 1 | x2 + 2x – 10 |
- 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.
Explanation & Answer
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Domain of Functions
•
Explain in your own words what the meaning of domain is. Also, explain why a
denominator cannot be zero.
The domain of a function is the set of values for which the function is defined. Another
perspective of this concept would be to indicate that it is the set of all the possible
independent values that a relation can have. It is the collection of all possible entries.
The denominator of a fraction can not be zero, since, as a division between expressions, this
would result in a mathematical indefinition, whose value would be + ∞ or -∞ depending on
the case, as shown in the following graph.
From the point of view of mathematical analysis, the indefinition of a division by zero can
be solved by the concept of limit. Suppose we have the following expression:
𝑓(𝑥) =
𝑛
𝑥
Where n is a natural number (other than zero). Then, to calculate the value of f (0), one can
use a boundary approximation, on the right:
𝑛
= +∞
→ + 0
𝑥0
𝑓(0) = lim
Or on the left:
𝑛
= −∞
→ − 0
𝑥0
𝑓(0) = lim
When the value of x tends to zero, n / x reaches an immensely large value (positive or
negative). It is usually expressed by say...
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