Question

Identify the square root function that has a range of (−∞,−5].(1 point)
Responses

y=x−3−−−−−√−5
𝑦
=
𝑥
−
3
−
5
y is equal to square root of x minus 3 end root minus 5

y=−−x−−−√−5
𝑦
=
−
−
𝑥
−
5
y is equal to negative square root of negative x minus 5

y=−x−3−−−−−√+5
𝑦
=
−
𝑥
−
3
+
5
y is equal to negative square root of x minus 3 end root plus 5

y=−x−−−√−5

Answer 1

To identify the square root function that has a range of (−∞,−5], we need to analyze the options provided.

1. **y = √(x - 3) - 5**:
- This function's range starts at -5 when x = 3 and goes to ∞ as x increases. Range: [-5, ∞). So this is **not** the correct function.

2. **y = -√(-x) - 5**:
- The square root function √(-x) is defined for x ≤ 0. The output of the negative square root function would be non-positive (i.e., ≤ 0). Therefore, y will produce values of (-∞, -5]. This function matches our required range.

3. **y = -√(x - 3) + 5**:
- The output of this function starts at 5 (when x = 3) and goes down to -∞ as x increases. Range: (-∞, 5]. So this is **not** the correct function.

4. **y = -√(-x) - 5** (duplicate):
- Same as option 2. We already established that it correctly has the range of (−∞,−5].

Thus, the correct function is:

**y = -√(-x) - 5**.