Describing End Behavior of Functions

Kendall Roberg introduces the concept of end behavior in functions, explaining how to describe what happens at the ends of a function using mathematical language. The video covers how functions approach positive and negative infinity as x increases or decreases, respectively. An example with a W-shaped graph is used to illustrate these concepts.

What does end behavior in mathematics describe?

• The intersection points of the function with axes

• The maximum and minimum values of a function

• The limits of a function as x approaches zero

• The behavior of a function at the ends of its graph

How is the end behavior of a function typically indicated on a graph?

• By shading the areas under the curve

• By dotted lines near the axes

• By arrows at the ends of the graph

• By labeling the intercepts

What happens to f(x) as x approaches positive infinity in the described function?

• f(x) approaches positive infinity

• f(x) approaches negative infinity

• f(x) remains constant

• f(x) approaches zero

As x increases, what is the behavior of f(x) in the context of the function discussed?

• f(x) approaches positive infinity

• f(x) approaches a constant value

• f(x) decreases

• f(x) oscillates

What does it mean when we say 'f(x) approaches positive infinity as x approaches positive infinity'?

• The function decreases without bound as x increases

• The function increases without bound as x increases

• The function oscillates as x increases

• The function remains constant as x increases

What is the behavior of the function as x approaches negative infinity?

• f(x) approaches zero

• f(x) approaches positive infinity

• f(x) approaches negative infinity

• f(x) remains constant

In the scenario where x is decreasing, what does f(x) approach?

• f(x) approaches a finite limit

• f(x) approaches negative infinity

• f(x) oscillates without bound

• f(x) approaches positive infinity

For the W-shaped graph, what is the end behavior of the function as x approaches positive infinity?

• f(x) approaches zero

• f(x) remains constant

• f(x) approaches negative infinity

• f(x) approaches positive infinity

What is the end behavior of the function on the W-shaped graph as x approaches negative infinity?

• f(x) approaches positive infinity

• f(x) approaches negative infinity

• f(x) approaches zero

• f(x) remains constant

In the context of the W-shaped graph, what is unique about its end behavior compared to a standard function?

• Both ends approach positive infinity

• One end approaches zero while the other approaches infinity

• Both ends approach zero

• Both ends approach negative infinity