A square root function has a domain of x greater than or equal to -4 and range of y grreater than or equal to 2. Which of the equations below match this description?
A. y= sqrt x-4 +2
B. y= sqrt x+4 +2
C. y= sqrt x-2 -4
D. y= sqrt x+2 -4
Hi. I don't got it. Whats the answer if you got it?
be careful with parentheses when typing equations
I think you mean
sqrt (x-4) + 2
To determine which equation matches the given domain and range, we need to evaluate the condition for both the domain and range.
The given domain is x greater than or equal to -4. This means that x values can be -4 or any value greater than -4.
The given range is y greater than or equal to 2. This means that y values can be 2 or any value greater than 2.
Now, let's analyze each equation using this information:
A. y = sqrt(x-4) + 2
For this equation, when we substitute x = -4, we get y = sqrt(-4-4) + 2 = sqrt(-8) + 2. Since the square root of a negative number is not a real number, this equation does not satisfy the condition for the domain. Therefore, it is not the correct equation.
B. y = sqrt(x+4) + 2
For this equation, when we substitute x = -4, we get y = sqrt(-4+4) + 2 = sqrt(0) + 2 = 0 + 2 = 2. This equation satisfies the condition for the range, as the minimum value of y is 2. Additionally, the value of x is -4, which is within the domain specified. Therefore, this equation matches the given description.
C. y = sqrt(x-2) - 4
For this equation, when we substitute x = -4, we get y = sqrt(-4-2) - 4 = sqrt(-6) - 4. This equation does not satisfy the condition for the domain, as the square root of a negative number is not a real number. Therefore, it is not the correct equation.
D. y = sqrt(x+2) - 4
For this equation, when we substitute x = -4, we get y = sqrt(-4+2) - 4 = sqrt(-2) - 4. This equation does not satisfy the condition for the domain, as the square root of a negative number is not a real number. Therefore, it is not the correct equation.
Based on our analysis, the equation that matches the given description is B. y = sqrt(x+4) + 2.