Positive/Negative and Increasing/Decreasing Intervals

Front

What is a negative interval in mathematics?

Back

A negative interval is a range of values where the function outputs are negative. For example, the interval (-∞, 1) indicates that all values less than 1 are included.

Front

What is a positive interval in mathematics?

Back

A positive interval is a range of values where the function outputs are positive. For example, the interval (1, ∞) indicates that all values greater than 1 are included.

Front

Define an increasing interval.

Back

An increasing interval is a range of x-values where the function's output values increase as x increases. For example, if f(x) is increasing on the interval (1, 4), then f(1) < f(2) < f(3) < f(4).

Front

Define a decreasing interval.

Back

A decreasing interval is a range of x-values where the function's output values decrease as x increases. For example, if f(x) is decreasing on the interval (4, 1), then f(4) > f(3) > f(2) > f(1).

Front

What does the interval (-∞, -3) represent?

Back

The interval (-∞, -3) represents all values less than -3, indicating a negative interval.

Front

What does the interval (4, 8) represent?

Back

The interval (4, 8) represents all values between 4 and 8, indicating a positive interval.

Front

How do you identify increasing intervals from a graph?

Back

To identify increasing intervals from a graph, look for sections where the graph rises as you move from left to right.

Front

How do you identify decreasing intervals from a graph?

Back

To identify decreasing intervals from a graph, look for sections where the graph falls as you move from left to right.

Front

What is the significance of critical points in determining intervals?

Back

Critical points are where the function changes from increasing to decreasing or vice versa. They help identify the boundaries of increasing and decreasing intervals.

Front

What is the interval notation for all real numbers?

Back

The interval notation for all real numbers is (-∞, ∞).