The correct answer is $\boxed{\text{D}}$.
The function $f(x) = e^{-x}(x^2 + x + 1)$ is a combination of three functions: $e^{-x}$, $x^2$, and $x + 1$. Each of these functions has its own characteristic graph.
The graph of $e^{-x}$ is a decreasing exponential function that approaches 0 as $x$ approaches $\infty$. The graph of $x^2$ is a parabola that opens up with a maximum point at $x = 0$. The graph of $x + 1$ is a straight line that increases linearly.
The graph of $f(x)$ is obtained by adding together the graphs of $e^{-x}$, $x^2$, and $x + 1$. The graph of $f(x)$ is a decreasing exponential function with a parabola-shaped hump in the middle. The hump is caused by the graph of $x^2$, which is positive for all values of $x$. The graph of $f(x)$ approaches 0 as $x$ approaches $\pm\infty$.
Here is a more detailed explanation of each option:
- Option A is the graph of $e^{-x}$. This is a decreasing exponential function that approaches 0 as $x$ approaches $\infty$.
- Option B is the graph of $x^2$. This is a parabola that opens up with a maximum point at $x = 0$.
- Option C is the graph of $x + 1$. This is a straight line that increases linearly.
- Option D is the graph of $f(x) = e^{-x}(x^2 + x + 1)$. This is a decreasing exponential function with a parabola-shaped hump in the middle. The hump is caused by the graph of $x^2$, which is positive for all values of $x$. The graph of $f(x)$ approaches 0 as $x$ approaches $\pm\infty$.