Question

Identify the square root function that is increasing over the interval [−3,∞).(1 point)
Responses

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

y=−x−3−−−−−−√+2
𝑦
=
−
𝑥
−
3
+
2
y is equal to square root of negative x minus 3 end root plus 2

y=x+3−−−−−√+2
𝑦
=
𝑥
+
3
+
2
y is equal to square root of x plus 3 end root plus 2

y=x−3−−−−−√+2

Answer 1

To identify the square root function that is increasing over the interval \([-3, ∞)\), let's analyze the given responses.

1. **\(y = -\sqrt{-x + 3}\)**:
The negative sign indicates that this function will be decreasing rather than increasing.

2. **\(y = -\sqrt{-x - 3} + 2\)**:
Similar to the first one, the negative sign indicates that this function is also decreasing.

3. **\(y = \sqrt{x + 3} + 2\)**:
The square root function \(\sqrt{x + 3}\) is an increasing function because the square root of a non-negative number increases as the input increases. This function is defined for \(x \geq -3\) and is therefore increasing over the interval \([-3, ∞)\).

4. **\(y = \sqrt{x - 3} + 2\)**:
This function is increasing for \(x \geq 3\), not for \([-3, ∞)\).

The only function that is increasing over the interval \([-3, ∞)\) is:
**\(y = \sqrt{x + 3} + 2\)**.