End Behavior and Extrema

Front

What is end behavior in a function?

Back

End behavior describes the behavior of the graph of a function as the input values (x) approach positive or negative infinity.

Front

What does it mean for a function to have a relative maximum?

Back

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

Front

How can you determine the number of relative maximums in a function?

Back

You can determine the number of relative maximums by analyzing the graph or using calculus to find critical points and test their nature.

Front

What is an extremum in the context of functions?

Back

An extremum is a point in the domain of a function where the function takes on a maximum or minimum value.

Front

What is the difference between relative and absolute extrema?

Back

Relative extrema are the highest or lowest points in a specific interval, while absolute extrema are the highest or lowest points over the entire domain of the function.

Front

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

Back

The end behavior of a polynomial function is determined by its leading term, which dictates whether the graph rises or falls as x approaches positive or negative infinity.

Front

What does it mean if a graph approaches y → ∞ as x → -∞?

Back

It means that as the x-values decrease without bound, the y-values of the function increase without bound.

Front

What is the significance of the leading coefficient in a polynomial function?

Back

The leading coefficient determines the direction of the graph's end behavior: if positive, the graph rises to the right; if negative, it falls to the right.

Front

How can you find the extrema of a function using calculus?

Back

You can find extrema by taking the derivative of the function, setting it to zero to find critical points, and using the second derivative test to classify them.

Front

What is the end behavior of a function if it approaches y → -∞ as x → ∞?

Back

It indicates that as x increases without bound, the function values decrease without bound.