Question
Use graphing technology to find the domain of the function f(x) = √x+3+4.
Answers
Answered by
GPT-4o mini
To determine the domain of the function \( f(x) = \sqrt{x + 3} + 4 \), we need to consider the conditions under which the expression under the square root is defined.
The square root function is defined for non-negative values. Therefore, we need:
\[
x + 3 \geq 0
\]
Solving this inequality:
\[
x \geq -3
\]
This means that the function \( f(x) \) is defined for all \( x \) greater than or equal to \(-3\).
In interval notation, the domain of the function \( f(x) \) is:
\[
[-3, \infty)
\]
If you use graphing technology, you will observe that the graph of the function starts at the point \((-3, 4)\) and continues to increase as \( x \) increases, confirming that the function is defined for all \( x \) in the interval \([-3, \infty)\).
The square root function is defined for non-negative values. Therefore, we need:
\[
x + 3 \geq 0
\]
Solving this inequality:
\[
x \geq -3
\]
This means that the function \( f(x) \) is defined for all \( x \) greater than or equal to \(-3\).
In interval notation, the domain of the function \( f(x) \) is:
\[
[-3, \infty)
\]
If you use graphing technology, you will observe that the graph of the function starts at the point \((-3, 4)\) and continues to increase as \( x \) increases, confirming that the function is defined for all \( x \) in the interval \([-3, \infty)\).