Question
Select the domain and range of the function below. You must pick one of each for credit.
(2 points)
Responses
{x | −2≤x <∞}
{x | −2≤x <∞}
{y | −∞<y<∞}
{y | −∞<y<∞}
{y | −∞<y ≤−2}
{y | −∞<y ≤−2}
{x | −∞<x <∞}
{x | −∞<x <∞}
{y | −2≤y <∞}
(2 points)
Responses
{x | −2≤x <∞}
{x | −2≤x <∞}
{y | −∞<y<∞}
{y | −∞<y<∞}
{y | −∞<y ≤−2}
{y | −∞<y ≤−2}
{x | −∞<x <∞}
{x | −∞<x <∞}
{y | −2≤y <∞}
Answers
Answer
Look at the equation below.
−10x+13+12x=5x−8
Which of the following steps could be used to transform the equation into the form x=a
, where a
is a number, to show that the equation has one solution?
Select TWO options that apply.
(2 points)
Responses
Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.
Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.
Add 5x to both sides of the equation and then simplify.
Add 5x to both sides of the equation and then simplify.
Add 8 to both sides of the equation and then simplify.
Add 8 to both sides of the equation and then simplify.
Subtract 13 from both sides of the equation and then simplify.
Subtract 13 from both sides of the equation and then simplify.
Subtract 10x from both sides of the equation and then simplify.
−10x+13+12x=5x−8
Which of the following steps could be used to transform the equation into the form x=a
, where a
is a number, to show that the equation has one solution?
Select TWO options that apply.
(2 points)
Responses
Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.
Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.
Add 5x to both sides of the equation and then simplify.
Add 5x to both sides of the equation and then simplify.
Add 8 to both sides of the equation and then simplify.
Add 8 to both sides of the equation and then simplify.
Subtract 13 from both sides of the equation and then simplify.
Subtract 13 from both sides of the equation and then simplify.
Subtract 10x from both sides of the equation and then simplify.
Answered by
GPT-4o mini
To accurately select the domain and range, we need to know the function that's being referred to. However, without additional information about the function, we can make some general assumptions based on the provided response options.
If we assume that the function is decreasing and approaches or has a minimum value of -2, like a function of the form \( f(x) = \sqrt{x + 2} \), then the domain and range could look like this:
- The domain: \( {x | -2 \leq x < ∞} \) (since x must be greater than or equal to -2 for the function to be defined)
- The range: \( {y | -2 \leq y < ∞} \) (if y starts at -2 and progresses toward positive infinity, which could happen for a function linked to x as above)
If we refer to a different function, please clarify which mathematical expression or function we need to analyze, so I can provide the correct domain and range.
If we assume that the function is decreasing and approaches or has a minimum value of -2, like a function of the form \( f(x) = \sqrt{x + 2} \), then the domain and range could look like this:
- The domain: \( {x | -2 \leq x < ∞} \) (since x must be greater than or equal to -2 for the function to be defined)
- The range: \( {y | -2 \leq y < ∞} \) (if y starts at -2 and progresses toward positive infinity, which could happen for a function linked to x as above)
If we refer to a different function, please clarify which mathematical expression or function we need to analyze, so I can provide the correct domain and range.
Answered by
GPT-4o mini
To transform the equation \(-10x + 13 + 12x = 5x - 8\) into the form \(x = a\), you can perform the following steps:
1. **Combine like terms** on the left side:
- Combine \(-10x\) and \(12x\) to get \(2x\).
- The equation then becomes \(2x + 13 = 5x - 8\).
2. After combining, you can isolate \(x\) by moving all terms involving \(x\) to one side and constant terms to the other side, effectively requiring you to:
- Subtract \(5x\) from both sides (or equivalently, you could choose to subtract the \(2x\) after combining terms).
Given the options, the following two responses will help in transforming the equation towards \(x = a\):
1. **Add 5x to both sides of the equation and then simplify.**
This will help isolate \(x\) on one side.
2. **Subtract 10x from both sides of the equation and then simplify.**
This effectively simplifies the equation by changing the terms accordingly.
The correct selections to achieve the goal of transforming the equation into the form \(x = a\) (where \(a\) is a specific number) would actually involve either choice mentioned above, depending on the approach. However, the most straightforward steps after combining terms already stated give you the necessary adjustments towards achieving the form \(x = a\).
So the correct answers, given the situation, are:
- **Add 5x to both sides of the equation and then simplify.**
- **Subtract 10x from both sides of the equation and then simplify.**
Just remember that after a suitable combination of terms, you will need to manipulate constants for a successful resolution.
1. **Combine like terms** on the left side:
- Combine \(-10x\) and \(12x\) to get \(2x\).
- The equation then becomes \(2x + 13 = 5x - 8\).
2. After combining, you can isolate \(x\) by moving all terms involving \(x\) to one side and constant terms to the other side, effectively requiring you to:
- Subtract \(5x\) from both sides (or equivalently, you could choose to subtract the \(2x\) after combining terms).
Given the options, the following two responses will help in transforming the equation towards \(x = a\):
1. **Add 5x to both sides of the equation and then simplify.**
This will help isolate \(x\) on one side.
2. **Subtract 10x from both sides of the equation and then simplify.**
This effectively simplifies the equation by changing the terms accordingly.
The correct selections to achieve the goal of transforming the equation into the form \(x = a\) (where \(a\) is a specific number) would actually involve either choice mentioned above, depending on the approach. However, the most straightforward steps after combining terms already stated give you the necessary adjustments towards achieving the form \(x = a\).
So the correct answers, given the situation, are:
- **Add 5x to both sides of the equation and then simplify.**
- **Subtract 10x from both sides of the equation and then simplify.**
Just remember that after a suitable combination of terms, you will need to manipulate constants for a successful resolution.