Exploring Polynomial Function End Behavior

The video tutorial covers polynomial functions, focusing on their characteristics and end behavior. It explains how the highest exponent in a polynomial determines the graph's end behavior, with odd exponents leading to opposite directions and even exponents resulting in the same direction. The tutorial provides examples of odd and even functions, illustrating their graphical representations. It also includes practice problems to reinforce understanding of polynomial graphs and their end behavior.

What is a polynomial function?

• A function with only even exponents.

• A function with no terms.

• A function with many terms.

• A function with only one term.

Which of the following is an example of a polynomial function?

• f(x) = sin(x)

• f(x) = x^2 + 3

• f(x) = sqrt(x)

• f(x) = log(x)

What determines the end behavior of a polynomial function?

• The coefficient of the first term.

• The highest exponent.

• The constant term.

• The number of terms.

For an odd exponent polynomial function, how do the ends of the graph behave?

• Ends stay constant.

• Both ends go up.

• Ends go in opposite directions.

• Both ends go down.

What is the end behavior of the function f(x) = -x^3 + 5?

• Both ends go up.

• Both ends go down.

• Starts down and goes up.

• Starts up and goes down.

How does the graph of a quadratic function behave at its ends?

• Ends go in opposite directions.

• Both ends go up or both go down.

• Ends stay constant.

• One end goes up and the other stays constant.

What is the end behavior of the function g(x) = -3(x+2)^2 + 1?

• Both ends go down.

• Ends stay constant.

• Both ends go up.

• Ends go in opposite directions.

For the function f(x) = x^5 - 3x^3 + x - 2, what is the end behavior?

• Ends stay constant.

• Both ends go down.

• Both ends go up.

• Ends go in opposite directions.

As x approaches infinity in the function f(x) = x^4 - 3x^2 - 3x, what happens to f(x)?

• f(x) stays constant.

• f(x) approaches negative infinity.

• f(x) oscillates.

• f(x) approaches positive infinity.

For the function f(x) = x^3 + 7x^2 + 16x, what is the end behavior as x approaches negative infinity?

• f(x) stays constant.

• f(x) approaches negative infinity.

• f(x) approaches positive infinity.

• f(x) oscillates.