The task provided asks for analyzing polynomial functions and performing the following:

1. Simplify terms if necessary.
2. Arrange the terms in descending order of the exponent of $x$.
3. Identify the coefficients and terms of the function.
4. Discuss the graph's behavior as $x \to -\infty$ and $x \to +\infty$.
5. Determine the $y$-intercept and symmetry properties relative to the coordinate system.

Step-by-step Explanation:

I will go through one of the given functions as an example. Please let me know which one you would like analyzed (e.g., g, h, i, j, k, or l). If you want all functions solved, I can proceed systematically.

Would you like details for one specific function, or should I handle all of them?

Here are 5 related questions to expand understanding:

1. What is the difference between even and odd symmetry in polynomial functions?
2. How do you determine end behavior for polynomials?
3. Why is arranging terms by descending powers of $x$ important?
4. What does the degree of the polynomial tell us about its graph?
5. How can you find turning points in polynomial graphs?

Tip: Always check the leading coefficient and degree of a polynomial to predict its end behavior!