Question

Question 8
What is the range of the relation below?
* {(-4,1)}, (-2,0), (8,-1)
1 point
Captionless Image
A. {-1, 1}
B. {-1, 0, 1}
C. {-4, -2, 8}
D. {-4, -2, -1, 0, 1, 8}
Question 9
What is the domain of the relation below?
*
1 point
Captionless Image
A. All real numbers greater than or equal to 0.
B. All real numbers.
C. All real numbers between -6 and 4.
D. All real numbers greater than -2.

Question 11
Given the function below, find the range for the domain {-3, -1, 1, 2}.
* g(x) = x^2 - 3
1 point
Captionless Image
A. {6, -2, 1}
B. {-6, -2, -1}
C. {-12, -4, 1, 4}
D. {-4, -2, 1, 4}
Question 12
For which value does f(x) = -5 ?
*
1 point
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A. x = -5
B. x = 1
C. x = -2
D. x = -1
E. x = 4
Question 13
Write an equation that represents the "n"th term of the sequence below using the explicit formula, aₙ=a₁ +(n-1)d.
* {2,-1, -4, -7...}
1 point
Captionless Image

A an=2n-5

B an=3n-1

C an = -3n - 10

D an = -3n + 5
Question 14
Given the sequence, find the 25th term.
* -1,3,7,11....
1 point
Captionless Image
A. 103
B. 99
C. 95
D. 91

Answer 1

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!