the range of which function includes -4?\n$y = \\sqrt{x}-5$\n$y = \\sqrt{x}+5$\n$y = \\sqrt{x + 5}$\n$y =…

Explanation:

Step1: Recall the property of square - root function

The square - root function $\sqrt{a}$ has the property that $\sqrt{a}\geq0$ for $a\geq0$.

Step2: Analyze each option

Option 1: $y = \sqrt{x}-5$

Let $y=-4$. Then $\sqrt{x}-5=-4$. Add 5 to both sides: $\sqrt{x}=-4 + 5=1$. Since $\sqrt{x}=1$ when $x = 1$ (because $1\geq0$), this is a valid solution.

Option 2: $y=\sqrt{x}+5$

If $y=-4$, then $\sqrt{x}+5=-4$. So, $\sqrt{x}=-4 - 5=-9$. But $\sqrt{x}\geq0$ for all $x\geq0$, so this equation has no solution.

Option 3: $y=\sqrt{x + 5}$

If $y=-4$, then $\sqrt{x + 5}=-4$. Since $\sqrt{x+5}\geq0$ for all $x\geq - 5$, this equation has no solution.

Option 4: $y=\sqrt{x-5}$

If $y=-4$, then $\sqrt{x - 5}=-4$. Since $\sqrt{x-5}\geq0$ for all $x\geq5$, this equation has no solution.

Answer:

$y=\sqrt{x}-5$