Question

what is the range of $y = \sqrt{x + 7} + 5$? $y \geq -7$ $y \geq -5$ all real numbers $y \geq 5$

Explanation:

Step1: Analyze the square root function

The square root function $\sqrt{x + 7}$ has a range of $y\geq0$ because the square root of a real number is always non - negative. So, $\sqrt{x + 7}\geq0$.

Step2: Analyze the transformed function

We have the function $y=\sqrt{x + 7}+5$. If we add 5 to both sides of the inequality $\sqrt{x + 7}\geq0$, we get $\sqrt{x + 7}+5\geq0 + 5$.
Simplifying the right - hand side, we have $\sqrt{x + 7}+5\geq5$, which means $y\geq5$.

Answer:

$y\geq5$ (the option with the text "$y\geq5$")