If the given term is the dominating term of a polynomial function, what can we conclude about each of the following features of the graph of the function? (a)domain (b)range (c)end behavior (d)number of zeros (e)number of turning points -9x6

Key Concepts

Dominating Term in Polynomials

The dominating term of a polynomial is the term with the highest degree, which significantly influences the polynomial's behavior as the input values become very large or very small. In the case of the polynomial -9x^6, the dominating term is -9x^6, indicating that the function will exhibit specific characteristics based on the degree and leading coefficient.

End Behavior of Polynomials

End behavior describes how the values of a polynomial function behave as the input approaches positive or negative infinity. For the polynomial -9x^6, since the leading term has an even degree and a negative coefficient, the ends of the graph will both point downwards, indicating that the function approaches negative infinity in both directions.

Number of Zeros and Turning Points

The number of zeros of a polynomial function corresponds to the x-intercepts of its graph, while turning points are where the graph changes direction. For a polynomial of degree 6, like -9x^6, it can have up to 6 zeros and up to 5 turning points, but the actual number may vary based on the specific polynomial's factors and behavior.