Polynomial Graphing

Front

What are the roots of the polynomial function f(x) = x^2(x - 2)^3(x - 7) and their multiplicities?

Back

0 (Multiplicity of 2), 2 (Multiplicity of 3), 7 (Multiplicity of 1)

Front

Write the equation of the function in factored form for the roots 0, -3, -1, and 2.

Back

f(x) = x(x + 3)(x + 1)(x - 2)

Front

What is the end behavior of the function y = -7x^4 + 7x^3 - 9x^2 + 10?

Back

As x → -∞, f(x) → -∞; As x → ∞, f(x) → -∞.

Front

What does a negative leading coefficient and an even degree indicate about the end behavior of a polynomial?

Back

The end arrows point in the same direction, both downwards.

Front

If the degree of a polynomial function is even, what can be said about its end behavior?

Back

The end arrows point in the same direction.

Front

Define the term 'multiplicity' in relation to polynomial roots.

Back

Multiplicity refers to the number of times a particular root appears in the factorization of a polynomial.

Front

What is the significance of the leading coefficient in a polynomial function?

Back

The leading coefficient determines the end behavior of the polynomial function.

Front

How do you determine the degree of a polynomial function?

Back

The degree is the highest power of the variable in the polynomial.

Front

What is the general form of a polynomial function?

Back

A polynomial function is expressed as f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

Front

What does it mean for a polynomial to be in factored form?

Back

A polynomial is in factored form when it is expressed as a product of its linear factors.