FC Increasing and Decreasing Practice

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points in that interval, the function's value at the second point is greater than the value at the first point.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, for any two points in that interval, the function's value at the second point is less than the value at the first point.

Front

How do you determine the intervals of increase or decrease from a graph?

Back

To determine intervals of increase or decrease from a graph, observe the slope of the graph: increasing intervals have a positive slope, while decreasing intervals have a negative slope.

Front

What is the significance of critical points in determining intervals of increase or decrease?

Back

Critical points are where the derivative is zero or undefined; they help identify potential intervals of increase or decrease.

Front

What is the derivative of a function?

Back

The derivative of a function represents the rate of change of the function with respect to its variable, indicating whether the function is increasing or decreasing.

Front

What is an interval notation?

Back

Interval notation is a way of writing subsets of the real number line, using parentheses for open intervals and brackets for closed intervals.

Front

What does the notation (-∞, 0) mean?

Back

The notation (-∞, 0) represents all real numbers less than 0, extending indefinitely to the left.

Front

What does the notation (1, ∞) mean?

Back

The notation (1, ∞) represents all real numbers greater than 1, extending indefinitely to the right.

Front

How do you express the union of two intervals?

Back

The union of two intervals is expressed using the symbol 'U', indicating that the solution includes all numbers from both intervals.

Front

What is the interval of increase for the function f(x) = x^2?

Back

The interval of increase for f(x) = x^2 is (0, ∞).