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 a non - negative output, i.e., $\sqrt{a}\geq0$ for $a\geq0$.

Step2: Analyze $y = \sqrt{x}-5$

Let $y=-4$. Then, set up the equation $\sqrt{x}-5=-4$. Add 5 to both sides of the equation: $\sqrt{x}=-4 + 5=1$. Since $x = 1\geq0$, when $x = 1$, $y=\sqrt{1}-5=1 - 5=-4$.

Step3: Analyze $y=\sqrt{x}+5$

Set $y=-4$, then $\sqrt{x}+5=-4$, so $\sqrt{x}=-4 - 5=-9$. But $\sqrt{x}\geq0$ for all $x\geq0$, so there is no solution for $x$.

Step4: Analyze $y=\sqrt{x + 5}$

Set $y=-4$, then $\sqrt{x + 5}=-4$. Since $\sqrt{x+5}\geq0$ for all $x\geq - 5$, there is no solution for $x$.

Step5: Analyze $y=\sqrt{x-5}$

Set $y=-4$, then $\sqrt{x - 5}=-4$. Since $\sqrt{x-5}\geq0$ for all $x\geq5$, there is no solution for $x$.

Answer:

$y=\sqrt{x}-5$