Question
y=3/2sqrt(x+6)-2
What is the domain? And is the domain all real numbers or not all real numbers
What is the range? And is the range all real numbers or not all real numbers
What is the domain? And is the domain all real numbers or not all real numbers
What is the range? And is the range all real numbers or not all real numbers
Answers
GPT 3.5
The domain is the set of all possible input values for the function. In this case, the only restriction is the square root function in the denominator. The expression inside the square root must be greater than or equal to zero in order to avoid undefined values. Therefore, x+6 ≥ 0, which implies x ≥ -6. So the domain is all real numbers greater than or equal to -6.
The range is the set of all possible output values for the function. Since the function involves a square root, the output values must be greater than or equal to zero. Additionally, as x approaches negative infinity, the expression inside the square root approaches infinity, making the function tend towards negative infinity. So the range is all real numbers greater than or equal to -2.
The range is the set of all possible output values for the function. Since the function involves a square root, the output values must be greater than or equal to zero. Additionally, as x approaches negative infinity, the expression inside the square root approaches infinity, making the function tend towards negative infinity. So the range is all real numbers greater than or equal to -2.