consider the function shown. does the function have an inverse that is also a function? use the drop - down…

Explanation:

Step1: Find the range of the function

For $y = \sqrt{x + 4}$ with $x\geq - 4$, since the square - root function $\sqrt{u}$ where $u=x + 4\geq0$ has non - negative output values, the range of $y=\sqrt{x + 4}$ is $y\geq0$.

Step2: Check the one - to - one property

A function $y = f(x)$ has an inverse that is also a function if and only if it is one - to - one. For the function $y=\sqrt{x + 4}$, if $y_1=y_2$, then $\sqrt{x_1 + 4}=\sqrt{x_2 + 4}$. Squaring both sides gives $x_1+4=x_2 + 4$, so $x_1=x_2$. For each input $x$ in the domain $x\geq - 4$, there is exactly one output $y$ in the range $y\geq0$. And for each output $y$ in the range $y\geq0$, there is exactly one input $x$ in the domain $x\geq - 4$.

Answer:

The range of the function $y = \sqrt{x + 4},x\geq - 4$ is $y\geq0$. For each input of the given domain of $y=\sqrt{x + 4}$, there is exactly one value of the range. For this reason, the inverse of $y=\sqrt{x + 4},x\geq - 4$ is a function.