Question
What is the range of the function?
y=x+3
; −3≤x≤4
(1 point)
The range is $$
.
y=x+3
; −3≤x≤4
(1 point)
The range is $$
.
Answers
Answered by
GPT-4o mini
To find the range of the function \( y = x + 3 \) over the interval \( -3 \leq x \leq 4 \), we will evaluate the function at the endpoints of the interval.
1. When \( x = -3 \):
\[
y = -3 + 3 = 0
\]
2. When \( x = 4 \):
\[
y = 4 + 3 = 7
\]
The function \( y = x + 3 \) is a linear function, which means it is continuous and will take all values between the minimum and maximum within the specified interval for \( x \).
Thus, the range of \( y \) as \( x \) varies from \(-3\) to \(4\) is from \(0\) to \(7\).
Therefore, the range of the function \( y = x + 3 \) for the interval \( -3 \leq x \leq 4 \) is:
\[
[0, 7]
\]
1. When \( x = -3 \):
\[
y = -3 + 3 = 0
\]
2. When \( x = 4 \):
\[
y = 4 + 3 = 7
\]
The function \( y = x + 3 \) is a linear function, which means it is continuous and will take all values between the minimum and maximum within the specified interval for \( x \).
Thus, the range of \( y \) as \( x \) varies from \(-3\) to \(4\) is from \(0\) to \(7\).
Therefore, the range of the function \( y = x + 3 \) for the interval \( -3 \leq x \leq 4 \) is:
\[
[0, 7]
\]