Positive/Negative and Increasing/Decreasing Intervals

Front

What is a negative interval in a function?

Back

A negative interval is a range of x-values where the function's output (y-values) is less than zero.

Front

Identify the negative interval for the function f(x) = x^2 - 3x - 2.

Back

The negative interval is (-2, 1).

Front

What does the interval (-∞, 1) represent in terms of function behavior?

Back

It represents a negative interval where the function values are below zero.

Front

What is an increasing interval in a function?

Back

An increasing interval is a range of x-values where the function's output (y-values) is increasing as x increases.

Front

Identify the increasing interval for the function f(x) = -x^2 + 4x.

Back

The increasing interval is (-∞, 2].

Front

What is the significance of the interval (4, 8) in a function?

Back

It indicates that the function is increasing between x = 4 and x = 8.

Front

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

Back

By finding the derivative of the function and analyzing where it is positive (increasing) or negative (decreasing).

Front

What is the relationship between critical points and increasing/decreasing intervals?

Back

Critical points are where the derivative is zero or undefined, and they help determine the boundaries of increasing and decreasing intervals.

Front

What does the notation (a, b) signify in interval notation?

Back

It signifies an open interval where a and b are not included in the interval.

Front

What does the notation [a, b] signify in interval notation?

Back

It signifies a closed interval where a and b are included in the interval.