x2 + 2x – 10/ 3x – 15
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
3x-15 = 0 when x=5
everything else is ok.
The domain of a function refers to the set of all possible input values for which the function is defined. In simpler terms, it is the set of values that can be plugged into a function to yield a valid output.
A denominator cannot be zero because division by zero is undefined in mathematics. When we divide by zero, we encounter an mathematical inconsistency that cannot be resolved. As a result, division by zero is considered mathematically illegal. Therefore, the denominator of a fraction cannot be zero.
Let's find the domain of the rational expression (x^2 + 2x - 10) / (3x - 15):
To determine the domain, we need to consider the values of x for which the denominator is non-zero. In this case, the denominator is 3x - 15. To find the excluded value, we need to set the denominator equal to zero and solve for x:
3x - 15 = 0
3x = 15
x = 5
So, the excluded value or value to be excluded from the domain is x = 5 because it makes the denominator zero.
The domain of this rational expression, in set notation, is all real numbers except x = 5. We can express it as:
Domain: {x ∈ R | x ≠ 5}
Now, let's find the domain of another rational expression:
To determine the domain for the second expression, we need to consider the values of x for which the denominator is non-zero. However, you haven't provided a specific rational expression in the question, so I cannot provide a specific answer.
In general, when dealing with rational expressions, we must find the excluded values that make the denominator zero by setting the denominator equal to zero and solving for x. These excluded values are then excluded from the domain. If there are no excluded values, it means the denominator is never zero, and no exclusions are necessary.
Now, let's incorporate the five math vocabulary words into the discussion:
1. The domain is the set of valid input values for a function.
2. An excluded value is a value that is not allowed in the domain due to it resulting in mathematical inconsistencies, such as division by zero.
3. The domain can be expressed in set notation, using curly brackets { } to enclose the valid values.
4. To find excluded values, we may need to factor the expression to identify the values that make the denominator zero.
5. The domain consists of real numbers, which are all numbers that can be expressed on the number line, including integers, fractions, decimals, and irrational numbers.