polynomial functions

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. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.

Front

What determines the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by its leading term, specifically the degree and the leading coefficient. If the degree is even and the leading coefficient is positive, the ends go up; if negative, the ends go down. If the degree is odd, the ends go in opposite directions.

Front

What is the maximum number of zeros a polynomial function can have?

Back

The maximum number of zeros a polynomial function can have is equal to its degree.

Front

How do you find the degree of a polynomial function?

Back

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

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 relative to nearby points.

Front

What is the difference between even and odd functions?

Back

An even function is symmetric about the y-axis (f(x) = f(-x)), while an odd function is symmetric about the origin (f(-x) = -f(x)).

Front

How can you determine if a polynomial function is even, odd, or neither?

Back

To determine if a polynomial function is even, check if f(x) = f(-x). For odd, check if f(-x) = -f(x). If neither condition holds, the function is neither even nor odd.

Front

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

Back

The leading coefficient affects the end behavior of the polynomial function. A positive leading coefficient indicates that the graph rises to the right, while a negative leading coefficient indicates that it falls to the right.

Front

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

Back

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

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What is a zero of a polynomial function?

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A zero of a polynomial function is a value of x for which f(x) = 0. It represents the x-intercepts of the graph.