Given the equation \( y=\sqrt{x+3}+4: \) What is the domain? \( \widehat{\approx} \)
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To find the domain of the equation \( y=\sqrt{x+3}+4 \), we need to ensure the expression inside the square root is non-negative. This means \( x + 3 \geq 0 \), leading to \( x \geq -3 \). Therefore, the domain of the function is all real numbers \( x \) such that \( x \) is greater than or equal to \(-3\), which can be expressed in interval notation as \( [-3, \infty) \). Another fun fact about square root functions: they often have a starting point or the "corner" of their graph, which is where the expression under the square root is zero. In this case, at \( x = -3 \), the function hits its minimum point—so if you're graphing, that's where the action starts! 🌟