Polynomial Operations and Function Properties

Front

What is an even function?

Back

A function f(x) is even if f(-x) = f(x) for all x in the domain of f. Graphically, even functions are symmetric about the y-axis.

Front

What is an odd function?

Back

A function f(x) is odd if f(-x) = -f(x) for all x in the domain of f. Graphically, odd functions are symmetric about the origin.

Front

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

Back

To determine if a polynomial function is even, check if all exponents of x are even. For odd, check if all exponents are odd. If neither condition is met, the function is neither.

Front

What are the steps to factor a quadratic polynomial?

Back

1. Identify the coefficients a, b, and c in ax^2 + bx + c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the middle term using these numbers. 4. Factor by grouping.

Front

What are the zeros of a polynomial function?

Back

The zeros of a polynomial function are the values of x for which f(x) = 0. They represent the x-intercepts of the graph.

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros of a quadratic function ax^2 + bx + c, use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

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. It determines the end behavior of the graph.

Front

What is a polynomial function of least degree?

Back

A polynomial function of least degree is the simplest polynomial that has the given zeros, with the smallest possible degree.

Front

How do you write a polynomial function given its zeros?

Back

If the zeros are r1, r2, ..., rn, the polynomial can be written as f(x) = a(x - r1)(x - r2)...(x - rn), where a is a non-zero constant.

Front

What is the difference between rational and irrational coefficients in polynomials?

Back

Rational coefficients are numbers that can be expressed as a fraction of two integers, while irrational coefficients cannot be expressed as such.