Precalculus Standard 4 Checkpoint

Front

What does it mean for a graph to be bounded?

Back

A graph is bounded if there exists a real number M such that the absolute value of the function is less than M for all values in its domain.

Front

What does it mean for a graph to be bounded above?

Back

A graph is bounded above if there exists a real number M such that the function values do not exceed M for all values in its domain.

Front

What does it mean for a graph to be bounded below?

Back

A graph is bounded below if there exists a real number m such that the function values are greater than or equal to m for all values in its domain.

Front

What does it mean for a graph to be not bounded?

Back

A graph is not bounded if it does not have upper or lower limits; the function values can increase or decrease indefinitely.

Front

How do you identify a local maximum on a graph?

Back

A local maximum occurs at a point where the function value is higher than the values of the function at nearby points.

Front

What is the significance of local maxima in a graph?

Back

Local maxima indicate points where the function reaches a peak in a specific interval, which can be important for optimization problems.

Front

What is the difference between a global maximum and a local maximum?

Back

A global maximum is the highest point over the entire domain of the function, while a local maximum is the highest point within a specific interval.

Front

How can you determine if a graph is bounded using its endpoints?

Back

If the function approaches finite values at both ends of its domain, it is likely bounded.

Front

What is the graphical representation of a bounded function?

Back

A bounded function will have its graph contained within horizontal lines (y = M and y = m) for all x in its domain.

Front

What is an example of a bounded function?

Back

f(x) = sin(x) is bounded because its values oscillate between -1 and 1.