Graphing Polynomials

Front

What is the y-intercept of the polynomial f(x) = x^3 - 5x^2 - 25x + 125?

Back

(0, 125)

Front

What two factors determine the end behavior of a polynomial?

Back

The degree and the leading coefficient.

Front

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

Back

A polynomial is even if all its terms have even degrees and odd if all its terms have odd degrees.

Front

What is the degree of the polynomial f(x) = -7x^3 + 11x^5 - 4x^6 + 113x?

Back

The degree is 6.

Front

What does the leading coefficient of a polynomial indicate about its end behavior?

Back

If the leading coefficient is positive, the right end goes up; if negative, the right end goes down.

Front

What is the general form of a polynomial function?

Back

f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where a_n ≠ 0.

Front

What is the significance of the constant term in a polynomial?

Back

The constant term represents the y-intercept of the polynomial.

Front

How do you find the x-intercepts of a polynomial?

Back

Set the polynomial equal to zero and solve for x.

Front

What is the difference between a polynomial and a rational function?

Back

A polynomial is a function that consists of variables raised to whole number powers, while a rational function is a ratio of two polynomials.

Front

What is the end behavior of the polynomial f(x) = 2x^4 - 3x^2 + 1?

Back

As x approaches ±∞, f(x) approaches +∞.