End Behavior of Polynomial Functions Explained

The video tutorial explains the concept of end behavior in functions, focusing on how graphs behave as x approaches positive or negative infinity. It covers the notation used to describe end behavior and examines specific cases for linear, quadratic, and higher-degree polynomial functions. The impact of negative coefficients on end behavior is also discussed, highlighting how they reverse the graph's direction. The tutorial concludes with a summary of end behavior patterns for odd and even functions, emphasizing the role of the leading coefficient.

What does the notation 'as x approaches infinity' signify?

• The graph goes down

• Moving to the left on the graph

• Moving to the right on the graph

• The graph goes up

If a graph goes up as x approaches infinity, what should you write?

• Undefined

• Positive infinity

• Zero

• Negative infinity

For the function y = x, what is the end behavior as x approaches negative infinity?

• The graph goes up

• The graph goes down

• The graph stays constant

• The graph oscillates

What is the end behavior of the function y = x^2 as x approaches negative infinity?

• The graph stays constant

• The graph goes down

• The graph goes up

• The graph oscillates

For the function y = x^3, what is the end behavior as x approaches positive infinity?

• The graph goes down

• The graph goes up

• The graph oscillates

• The graph stays constant

What is the end behavior of the function y = x^4 as x approaches negative infinity?

• The graph oscillates

• The graph goes up

• The graph goes down

• The graph stays constant

How does the end behavior change if the function y = x is modified to y = -x?

• The graph stays constant

• The graph goes down to the right and up to the left

• The graph goes up to the right and down to the left

• The graph oscillates

What happens to the end behavior of y = x^2 when it is changed to y = -x^2?

• The graph stays constant

• The graph goes up on both sides

• The graph oscillates

• The graph goes down on both sides

For an odd function with a positive leading coefficient, what is the end behavior?

• Up on both sides

• Down on both sides

• Down to the right, up to the left

• Up to the right, down to the left

For an even function with a negative leading coefficient, what is the end behavior?

• Up to the right, down to the left

• Down to the right, up to the left

• Up on both sides

• Down on both sides