Sure! Here are the answers to your questions:
Question 8: The range of the relation {(-4,1), (-2,0), (8,-1)} consists of the second elements of the ordered pairs. Thus, the range is:
- Range: {1, 0, -1} So the answer is: B. {-1, 0, 1}
Question 9: Since there is no specific relation provided to evaluate, we'll assume the context of common domain types. Without the image, it’s difficult to give a definite answer, but assuming typical constraints for a relation:
- A common answer for a domain that covers possibly all scenarios without additional context could often be: B. All real numbers.
Question 11: The function is given by g(x) = x² - 3. We need to calculate this for the values in the specified domain {-3, -1, 1, 2}:
- For x = -3: g(-3) = (-3)² - 3 = 9 - 3 = 6
- For x = -1: g(-1) = (-1)² - 3 = 1 - 3 = -2
- For x = 1: g(1) = (1)² - 3 = 1 - 3 = -2
- For x = 2: g(2) = (2)² - 3 = 4 - 3 = 1
The results are {6, -2, -2, 1} and the unique values are {-2, 1, 6}. So the answer is: D. {-4, -2, 1, 4} (It looks like this choice does not reflect the computed values correctly; please check the options.)
Question 12: To determine for which value f(x) = -5, we would need the expression for f(x). As that isn't provided, I can't accurately answer this question unless you provide additional information.
Question 13: To find the explicit formula for the sequence {2, -1, -4, -7...}, we first note that it has a starting term \(a_1 = 2\) and a common difference \(d = -3\): Using the formula \(a_n = a_1 + (n-1)d\):
- aₙ = 2 + (n-1)(-3)
- aₙ = 2 - 3n + 3
- aₙ = -3n + 5.
The correct answer is: D. aₙ = -3n + 5
Question 14: The sequence -1, 3, 7, 11... is arithmetic with a first term \(a_1 = -1\) and a common difference \(d = 4\). Using the formula for the nth term: \[a_n = a_1 + (n-1)d\] So:
- aₙ = -1 + (n-1)(4) = -1 + 4n - 4 = 4n - 5.
For the 25th term, calculate \(a_{25}\):
- a₂₅ = 4(25) - 5 = 100 - 5 = 95.
The answer is: C. 95
If there is anything more specific you would like help with or if any details are missing, feel free to provide more context!