Extrema and end behavior

Front

What is a relative maximum?

Back

A relative maximum is a point on a graph where the function value is higher than the values of the function at nearby points.

Front

What does the notation x → -∞ signify?

Back

It indicates that x is approaching negative infinity, meaning it is getting larger in the negative direction.

Front

What does the notation x → ∞ signify?

Back

It indicates that x is approaching positive infinity, meaning it is getting larger in the positive direction.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior can be determined by the leading term of the polynomial. If the leading coefficient is positive and the degree is even, both ends go up. If the leading coefficient is negative and the degree is even, both ends go down.

Front

What is the end behavior of a function if both ends go to infinity?

Back

If both ends go to infinity, it can be expressed as: x → -∞, f(x) → ∞ and x → ∞, f(x) → ∞.

Front

What is the end behavior of a function if one end goes to infinity and the other goes to negative infinity?

Back

If one end goes to infinity and the other goes to negative infinity, it can be expressed as: x → -∞, f(x) → ∞ and x → ∞, f(x) → -∞.

Front

What is an extremum?

Back

An extremum is a point in a function where it reaches a local maximum or minimum.

Front

How can you find the number of extrema in a graph?

Back

You can find the number of extrema by identifying the peaks (maxima) and valleys (minima) in the graph.

Front

What is the significance of the leading coefficient in determining end behavior?

Back

The leading coefficient determines the direction of the ends of the graph. A positive leading coefficient means the right end goes up, while a negative leading coefficient means the right end goes down.

Front

What does it mean if a function has three extrema?

Back

It means the graph has three points where it reaches either a local maximum or minimum.