Graphs of Polynomials

Front

What is the degree of a polynomial function?

Back

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

Front

How do you determine the degree of a polynomial from its graph?

Back

The degree can be determined by observing 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 general form of a polynomial function?

Back

The general form of a polynomial function is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

Front

What does the leading coefficient of a polynomial indicate?

Back

The leading coefficient indicates the direction of the graph as x approaches positive or negative infinity.

Front

What is the significance of the roots of a polynomial function?

Back

The roots of a polynomial function are the values of x for which the function equals zero; they correspond to the x-intercepts of the graph.

Front

How can you find the roots of a polynomial function?

Back

Roots can be found by factoring the polynomial, using the quadratic formula, or applying numerical methods for higher degree polynomials.

Front

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

Back

A polynomial of degree n can have at most n roots, counting multiplicities.

Front

What is a turning point in the context of polynomial graphs?

Back

A turning point is a point on the graph where the function changes direction from increasing to decreasing or vice versa.

Front

How does the end behavior of a polynomial function relate to its degree and leading coefficient?

Back

The end behavior is determined by the degree and leading coefficient: if the degree is even, both ends go in the same direction; if odd, they go in opposite directions.

Front

What is the difference between a polynomial function and a rational function?

Back

A polynomial function is a function that can be expressed as a polynomial, while a rational function is a ratio of two polynomial functions.