Function Behavior

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you express a domain interval using inequality notation?

Back

A domain interval can be expressed using inequality notation by indicating the lower and upper bounds of the interval, such as 'a < x ≤ b'.

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

Front

What does it mean for a function to be decreasing on an interval?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) > f(x2).

Front

What does it mean for a function to be constant on an interval?

Back

A function is constant on an interval if the output value (y) does not change for any input value (x) within that interval.

Front

How can you determine the intervals of increase and decrease for a function?

Back

To determine the intervals of increase and decrease, analyze the first derivative of the function: where the derivative is positive, the function is increasing; where it is negative, the function is decreasing.

Front

What is the significance of critical points in analyzing function behavior?

Back

Critical points are values of x where the derivative is zero or undefined; they help identify potential local maxima, minima, and points of inflection.

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include its endpoints, while a closed interval [a, b] includes its endpoints.

Front

How do you represent a union of intervals in interval notation?

Back

A union of intervals is represented in interval notation by using the symbol 'U', such as (-3, 0) U (2, 3).