Finding the end behavior of a polynomial to the fifth degree

The video tutorial explains the concept of end behavior in polynomials, focusing on how the degree and leading coefficient determine the graph's behavior as x approaches positive or negative infinity. It covers both even and odd degree polynomials, using quadratics and cubics as examples, and discusses how to express end behavior using different notations.

What two factors are crucial in determining the end behavior of a polynomial function?

• The degree and the constant term

• The degree and the leading coefficient

• The leading coefficient and the constant term

• The number of terms and the degree

For an even-degree polynomial, what determines if the graph opens upwards?

• The number of terms being even

• The leading coefficient being positive

• The constant term being positive

• The degree being positive

How does the graph of an odd-degree polynomial behave if the leading coefficient is positive?

• Rises left, falls right

• Falls left, rises right

• Rises left, rises right

• Falls left, falls right

What is the end behavior of a positive odd-degree polynomial as x approaches negative infinity?

• f(x) remains constant

• f(x) approaches negative infinity

• f(x) oscillates

• f(x) approaches positive infinity

In alternative notation, how is the end behavior of a polynomial described as x approaches infinity?

• As x approaches infinity, f(x) remains constant

• As x approaches infinity, f(x) approaches negative infinity

• As x approaches infinity, f(x) approaches infinity

• As x approaches infinity, f(x) approaches zero