1. We are asked to analyze the expression $$e^{\sqrt{2x}+2}$$. 2. This is an exponential function with base $e$ (Euler's number) raised to the power of the sum of $\sqrt{2x}$ and 2. 3. The exponent can be rewritten as $$\sqrt{2x} + 2$$, which means the output depends on both the square root of $2x$ and a constant addition of 2. 4. Important considerations: - The domain must satisfy $2x \geq 0$ to keep the square root defined, so $$x \geq 0$$. - As $x$ increases, $\sqrt{2x}$ increases, so the exponent and thus the function value increase. 5. The function is continuous and positive for $x \geq 0$. 6. Final expression: $$y = e^{\sqrt{2x} + 2}$$