Positive/Negative and Increasing/Decreasing Intervals

Front

What are increasing intervals in a function?

Back

Increasing intervals are ranges of the independent variable (x-values) where the function's output (y-values) is rising as x increases.

Front

What are decreasing intervals in a function?

Back

Decreasing intervals are ranges of the independent variable (x-values) where the function's output (y-values) is falling as x increases.

Front

How do you identify increasing and decreasing intervals from a graph?

Back

Increasing intervals are identified where the graph slopes upwards, while decreasing intervals are where the graph slopes downwards.

Front

What does the interval notation (-∞, -3) signify?

Back

The interval (-∞, -3) indicates all x-values less than -3, extending indefinitely to the left on the number line.

Front

What does the interval notation (-2, ∞) signify?

Back

The interval (-2, ∞) indicates all x-values greater than -2, extending indefinitely to the right on the number line.

Front

What is the significance of the point where a function changes from increasing to decreasing?

Back

This point is known as a local maximum, where the function reaches its highest value before decreasing.

Front

What is the significance of the point where a function changes from decreasing to increasing?

Back

This point is known as a local minimum, where the function reaches its lowest value before increasing.

Front

How can you determine if a function is positive or negative over an interval?

Back

A function is positive over an interval if its output (y-values) is above the x-axis, and negative if its output is below the x-axis.

Front

What is the role of critical points in determining increasing and decreasing intervals?

Back

Critical points, where the derivative is zero or undefined, help identify potential locations where the function changes from increasing to decreasing or vice versa.

Front

What does the interval notation (2, ∞) signify?

Back

The interval (2, ∞) indicates all x-values greater than 2, extending indefinitely to the right on the number line.