Polynomial Functions End Behavior

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

What determines the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the degree of the polynomial and the sign of the leading coefficient.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How do you find the degree of a polynomial?

Back

The degree of a polynomial is found by identifying the highest power of the variable in the polynomial.

Front

What are the zeros of a polynomial function?

Back

The zeros of a polynomial function are the values of the variable that make the polynomial equal to zero.

Front

What is the significance of the multiplicity of a zero?

Back

The multiplicity of a zero indicates how many times that zero is repeated as a root of the polynomial.

Front

What is a relative extremum?

Back

A relative extremum is a point on the graph of a function where the function takes on a maximum or minimum value compared to nearby points.

Front

How can you determine the number of relative extrema in a polynomial function?

Back

The number of relative extrema can be determined by analyzing the critical points, which are found by taking the derivative and setting it to zero.

Front

What is the end behavior of a polynomial function with an even degree and a positive leading coefficient?

Back

The end behavior will rise to positive infinity on both ends.

Front

What is the end behavior of a polynomial function with an odd degree and a negative leading coefficient?

Back

The end behavior will fall to negative infinity on the right and rise to positive infinity on the left.