Function Analysis

Front

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

Back

As x → -∞, f(x) → -∞ and as x → ∞, f(x) → ∞.

Front

What are the zeros of the function f(x) = (x + 3)(x + 1)(x - 2)(x - 5)?

Back

-3, -1, 2, 5.

Front

Define a polynomial function's degree.

Back

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

Front

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

Back

As x → -∞, f(x) → ∞ and as x → ∞, f(x) → ∞.

Front

What does it mean for a function to have local maxima?

Back

Local maxima are points where the function value is higher than the values of the function at nearby points.

Front

How do you determine the number of local maxima and minima in a polynomial function?

Back

By analyzing the first derivative of the function and finding critical points.

Front

What is a leading coefficient in a polynomial function?

Back

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

Front

What is the significance of the leading coefficient's sign?

Back

The sign of the leading coefficient determines the end behavior of the polynomial function.

Front

What is the difference between even and odd degree polynomials?

Back

Even degree polynomials have symmetrical end behavior, while odd degree polynomials have opposite end behavior.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have at most n real zeros.