1. The problem asks where the curve of the function $y = 3e^{x} + 1$ will go after sketching the graph. 2. The function is an exponential function with base $e$, scaled by 3 and shifted upward by 1. 3. Important properties of $y = 3e^{x} + 1$: - As $x \to \infty$, $e^{x} \to \infty$, so $y \to \infty$. - As $x \to -\infty$, $e^{x} \to 0$, so $y \to 1$ (the horizontal asymptote). 4. This means the curve will rise steeply to infinity as $x$ increases and approach the line $y=1$ from above as $x$ decreases. 5. The graph never crosses the horizontal asymptote $y=1$. 6. The function is always positive and increasing because $3e^{x} > 0$ for all $x$. Final answer: The curve will rise rapidly to infinity as $x$ increases and approach the horizontal asymptote $y=1$ as $x$ decreases.