Graphing 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.

Front

What does the degree of a polynomial indicate?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial.

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 can you determine if a polynomial function is even or odd?

Back

A polynomial function is even if f(-x) = f(x) for all x, and odd if f(-x) = -f(x) for all x.

Front

What does it mean if a zero of a polynomial has an even multiplicity?

Back

If a zero has an even multiplicity, the graph will touch the x-axis at that zero and turn around.

Front

What does it mean if a zero of a polynomial has an odd multiplicity?

Back

If a zero has an odd multiplicity, the graph will cross the x-axis at that zero.

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its linear factors.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros, set the polynomial equal to zero and solve for the variable.

Front

What is the significance of the x-intercepts of a polynomial graph?

Back

The x-intercepts represent the zeros of the polynomial function where the graph crosses the x-axis.

Front

What is the end behavior of a polynomial function?

Back

The end behavior describes how the graph behaves as x approaches positive or negative infinity.