Final answer:
The graph of f(x) = 4x⁷ + 40x⁶ + 100x⁵ is a 7th-degree polynomial function with a positive leading coefficient, possibly with up to 6 turning points, and will pass through the origin.
Step-by-step explanation:
The statement that describes the graph of f(x) = 4x⁷ + 40x⁶ + 100x⁵ would indicate that it is a polynomial function of degree 7. Since the leading term is 4x⁷ and the leading coefficient (4) is positive, the end behavior of the graph is as follow: as x approaches negative infinity, f(x) approaches negative infinity, and as x approaches positive infinity, f(x) approaches positive infinity.
Additionally, this function has no constant term, which means it will pass through the origin (0, 0). The graph may also have up to 6 turning points as a 7th-degree polynomial can have at most n-1 turning points, where n is the degree of the polynomial.
Graphing this function would require identifying all the real zeros or roots by possibly using numerical methods or graphing technology because the degree is too high for simple analytical solutions.