Graphing Polynomials

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

Front

Define the leading coefficient of a polynomial.

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It influences the end behavior of the graph.

Front

What does it mean for a polynomial to have an even degree?

Back

A polynomial has an even degree if the highest exponent of its variable is an even number. The end behavior of even-degree polynomials is the same on both ends (either both go to +∞ or both go to -∞).

Front

What does it mean for a polynomial to have an odd degree?

Back

A polynomial has an odd degree if the highest exponent of its variable is an odd number. The end behavior of odd-degree polynomials is opposite on both ends (one goes to +∞ and the other to -∞).

Front

Back

As x approaches -∞, f(x) approaches -∞; as x approaches +∞, f(x) also approaches -∞.

Front

What is multiplicity in the context of polynomial roots?

Back

Multiplicity refers to the number of times a particular root appears in a polynomial. A root with an even multiplicity will touch the x-axis, while a root with an odd multiplicity will cross the x-axis.

Front

What is the factored form of a polynomial?

Back

Front

What is the significance of the y-intercept in a polynomial graph?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating f(0). It provides information about the polynomial's value at x = 0.

Front

How can you identify the degree of a polynomial from its graph?

Back

The degree of a polynomial can be identified by the number of turning points in the graph. A polynomial of degree n can have at most n-1 turning points.

Front

What is the relationship between the number of roots and the degree of a polynomial?

Back

A polynomial of degree n can have up to n real roots, counting multiplicities.