Question
Part of a line is graphed. The points are (2,1), which is open-circled, and (6,-3), which is closed-circled. Which inequalities could describe the domain and range?
A: Domain: 2<x<6. Range: 2<y<6
B: Domain: 2< x is less than or greater to 6. Range: -3, is less than or equal to y < 1
C: Domain: 2 is less than or equal to x < 6. Range: y < 1
D: Domain: x is greater than or equal to 2. Range: -3 < y is less than or equal to 1.
A: Domain: 2<x<6. Range: 2<y<6
B: Domain: 2< x is less than or greater to 6. Range: -3, is less than or equal to y < 1
C: Domain: 2 is less than or equal to x < 6. Range: y < 1
D: Domain: x is greater than or equal to 2. Range: -3 < y is less than or equal to 1.
Answers
GPT-4o mini
To determine the correct inequalities that describe the domain and range based on the given points:
1. The point (2,1) is open-circled, which means that 2 is **not** included in the domain, and the y-value of 1 is also **not** included in the range.
2. The point (6,-3) is closed-circled, which means that 6 **is** included in the domain, and the y-value of -3 **is** included in the range.
From this information, we can derive the inequalities:
- For the **domain**, since 2 is not included and 6 is included, the inequality is \(2 < x \leq 6\).
- For the **range**, since -3 is included and 1 is not included, the inequality is \(-3 \leq y < 1\).
Now, let's evaluate the options:
A: Domain: \(2 < x < 6\). Range: \(2 < y < 6\)
**Incorrect** - The domain should include 6, and the range does not match the values we have.
B: Domain: \(2 < x \) is less than or equal to 6. Range: \(-3 \leq y < 1\)
**Incorrect** - This wording is a bit confusing, but generally, it suggests that 6 is included, which is good, but it does not align with the conventional format.
C: Domain: \(2 \leq x < 6\). Range: \(y < 1\)
**Incorrect** - 2 should not be included in the domain, and the range is incomplete as it does not cover -3.
D: Domain: \(x \geq 2\). Range: \(-3 < y \leq 1\)
**Incorrect** - The domain incorrectly includes 2, and the range incorrectly includes values greater than -3.
Combining our evaluation:
- The correct inequalities would be:
- Domain: \(2 < x \leq 6\)
- Range: \(-3 \leq y < 1\)
However, none of the options perfectly match this setup. The closest correct conditions might be:
B: Assuming "is less than or equal to" helps imply it includes 6 correctly, though it's not typically stated this way. D is almost correct but fails the domain inclusion for 2.
So the best interpretation, if forced to choose, from those offered (and rephrasing poorly worded statements), is:
**B** assuming slight leniency in inferring meanings from the equations provided.
1. The point (2,1) is open-circled, which means that 2 is **not** included in the domain, and the y-value of 1 is also **not** included in the range.
2. The point (6,-3) is closed-circled, which means that 6 **is** included in the domain, and the y-value of -3 **is** included in the range.
From this information, we can derive the inequalities:
- For the **domain**, since 2 is not included and 6 is included, the inequality is \(2 < x \leq 6\).
- For the **range**, since -3 is included and 1 is not included, the inequality is \(-3 \leq y < 1\).
Now, let's evaluate the options:
A: Domain: \(2 < x < 6\). Range: \(2 < y < 6\)
**Incorrect** - The domain should include 6, and the range does not match the values we have.
B: Domain: \(2 < x \) is less than or equal to 6. Range: \(-3 \leq y < 1\)
**Incorrect** - This wording is a bit confusing, but generally, it suggests that 6 is included, which is good, but it does not align with the conventional format.
C: Domain: \(2 \leq x < 6\). Range: \(y < 1\)
**Incorrect** - 2 should not be included in the domain, and the range is incomplete as it does not cover -3.
D: Domain: \(x \geq 2\). Range: \(-3 < y \leq 1\)
**Incorrect** - The domain incorrectly includes 2, and the range incorrectly includes values greater than -3.
Combining our evaluation:
- The correct inequalities would be:
- Domain: \(2 < x \leq 6\)
- Range: \(-3 \leq y < 1\)
However, none of the options perfectly match this setup. The closest correct conditions might be:
B: Assuming "is less than or equal to" helps imply it includes 6 correctly, though it's not typically stated this way. D is almost correct but fails the domain inclusion for 2.
So the best interpretation, if forced to choose, from those offered (and rephrasing poorly worded statements), is:
**B** assuming slight leniency in inferring meanings from the equations provided.