Question

Consider the function y = √x - 5.

What are the domain and range of this function?

O domain: x ≤ 5, range: y ≥ 0
O domain: x ≥ 0, range: y ≥ 5
O domain: x ≥ 5, range: y ≥ 0
O domain: x ≤ 0, range: y ≥ 5

Answer 1

The function y = √x - 5 has a domain of x ≥ 5 because a square root requires non-negative input. The range is y ≥ 0 since subtracting 5 from a square root still produces non-negative outputs. Considering as a, b, c and d option number c is correct.

Step-by-step explanation:

The function in question is y = √x - 5. To determine the correct domain and range for this function, we must consider the properties of square roots and subtraction. The square root function, √x, is only real and defined for x values that are greater than or equal to 0, meaning x cannot be negative. Therefore, considering the transformation by subtracting 5, the domain must start at the point where the value inside the square root becomes non-negative, which in this case is x = 5.

This means that the domain of the function is x ≥ 5. As for the range, since the square root function produces non-negative outputs and we are subtracting 5 afterwards, the smallest value y can take is when x equals 5, which gives us y = √5 - 5. So y should also be non-negative as the square root cannot be negative; thus, the range of the function is y ≥ 0.