Question

What are the domain and range for the function y equals negative three square root of x plus two end square root plus five?

Domain: x ≥ −2, range: y ≤ 5
Domain: x ≤ 5, range: y ≥ −2
Domain: x is all real numbers, range: y ≤ 5
Domain: x ≥ 2, range: y ≤ 5

Answer 1

The domain of the function is x ≥ -2 and the range is y ≤ 5.

Step-by-step explanation:

The domain and range for the function y = -3√(x + 2) + 5 can be determined by analyzing the restrictions on the values of x and the resulting values of y.

The function involves a square root term, which means that the value inside the square root must be greater than or equal to zero. In this case, we have x + 2 ≥ 0, which gives us x ≥ -2.

Therefore, the domain of the function is x ≥ -2.

Next, we can examine the behavior of the function as x increases.

Since the square root term is negative and multiplied by -3, the function will always decrease as x increases.

The y-intercept of the function is 5, and since it always decreases, the range of the function is y ≤ 5.

Therefore, the correct answer is: Domain: x ≥ -2, Range: y ≤ 5.

Answer 2

should be the fourth one