Question
What is the range when the domain is restricted to [-2, 1]?
Answers
GPT-4o mini
To determine the range of a function when the domain is restricted to \([-2, 1]\), we first need to know the function itself. Please provide the function you would like to analyze, and I can help you find the range over the specified domain.
Tilly
y=3x+5
GPT-4o mini
To find the range of the function \( y = 3x + 5 \) when the domain is restricted to \([-2, 1]\), we can follow these steps:
1. **Substitute the endpoints of the domain into the function** to find the corresponding \( y \) values.
- For \( x = -2 \):
\[
y = 3(-2) + 5 = -6 + 5 = -1
\]
- For \( x = 1 \):
\[
y = 3(1) + 5 = 3 + 5 = 8
\]
2. **Identify the range**: The function \( y = 3x + 5 \) is a linear function, which means it continuously increases (since the coefficient of \( x \) is positive). Therefore, the range will extend from the minimum \( y \) value to the maximum \( y \) value calculated at the endpoints of the domain.
From the calculations:
- The minimum value when \( x = -2 \) is \( -1 \).
- The maximum value when \( x = 1 \) is \( 8 \).
3. **Conclusion**: The range of the function \( y = 3x + 5 \) when the domain is restricted to \([-2, 1]\) is \([-1, 8]\).
Thus, the range is \([-1, 8]\).
1. **Substitute the endpoints of the domain into the function** to find the corresponding \( y \) values.
- For \( x = -2 \):
\[
y = 3(-2) + 5 = -6 + 5 = -1
\]
- For \( x = 1 \):
\[
y = 3(1) + 5 = 3 + 5 = 8
\]
2. **Identify the range**: The function \( y = 3x + 5 \) is a linear function, which means it continuously increases (since the coefficient of \( x \) is positive). Therefore, the range will extend from the minimum \( y \) value to the maximum \( y \) value calculated at the endpoints of the domain.
From the calculations:
- The minimum value when \( x = -2 \) is \( -1 \).
- The maximum value when \( x = 1 \) is \( 8 \).
3. **Conclusion**: The range of the function \( y = 3x + 5 \) when the domain is restricted to \([-2, 1]\) is \([-1, 8]\).
Thus, the range is \([-1, 8]\).