Question

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

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

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

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

y=√-x - 5

Answer 1

To identify the correct square root function with a range of (−∞, −5], we need to analyze the transformations implied by each option.

1. **y = -√(x - 3) + 5**:
- The square root function √(x - 3) has a range of [0, ∞).
- By applying a negative sign, the range becomes (−∞, 0].
- Lastly, shifting it up by 5 yields a range of (−∞, 5].
- This does not meet the condition we need.

2. **y = -√(-x - 5)**:
- The square root function √(-x - 5) is not defined for x > -5.
- It has a range of [0, ∞), which when negated becomes (−∞, 0].
- This function also does not meet the condition.

3. **y = √(x - 3) - 5**:
- The square root function has a range of [0, ∞).
- When you subtract 5, the range becomes [-5, ∞).
- This does not meet our condition.

4. **y = √(-x) - 5**:
- The square root function √(-x) is defined for x ≤ 0 and has a range of [0, ∞).
- When you subtract 5, the range becomes [-5, ∞).
- This also does not meet our condition.

None of the given options seem to yield the correct range of (−∞, −5].

For a function f(x) with a range of (−∞, −5], it would typically have a parent function modified appropriately with a vertical shift downwards and possibly an inversion.

To achieve a range of (−∞, −5], you might consider a function of the form:

y = -√(x) - 5 or a similar modification.

It appears that none of the provided responses are appropriate for the specified range.