Key Features and Classifying Polynomials

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 are the key features of polynomial functions?

Back

Key features include degree, leading coefficient, end behavior, and turning points.

Front

How do you determine the degree of a polynomial?

Back

The degree of a polynomial is determined by the highest power of the variable in the expression.

Front

What does the leading coefficient of a polynomial indicate?

Back

The leading coefficient indicates the direction of the end behavior of the polynomial function.

Front

What is end behavior in the context of polynomial functions?

Back

End behavior describes how the values of a polynomial function behave as the input approaches positive or negative infinity.

Front

What is a quartic function?

Back

A quartic function is a polynomial function of degree four.

Front

How can you identify the number of turning points in a polynomial function?

Back

The maximum number of turning points of a polynomial function is one less than its degree.

Front

What is the significance of turning points in polynomial graphs?

Back

Turning points indicate where the graph changes direction, which can affect the function's local maxima and minima.

Front

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

Back

As x approaches ±∞, the function approaches +∞.

Front

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

Back

As x approaches -∞, the function approaches +∞ and as x approaches +∞, the function approaches -∞.