Intervals of Functions

Front

What are the types of intervals that a function can demonstrate?

Back

Increasing, constant, decreasing.

Front

Where is a function constant on its graph?

Back

The function is constant in the interval where the y-value does not change as x changes.

Front

What does it mean for a function to have a positive slope?

Back

A positive slope indicates that as x increases, the value of f(x) also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing when the value of f(x) decreases as x increases.

Front

How can you identify intervals of increase and decrease on a graph?

Back

By observing the direction of the graph: rising indicates increasing, falling indicates decreasing.

Front

What is the significance of constant intervals in a function?

Back

Constant intervals indicate that the function's output remains the same over a range of input values.

Front

How do you determine the slope of a function on a graph?

Back

The slope is determined by the rise over run between two points on the graph.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include endpoints, while closed intervals include endpoints.

Front

How can you express an interval where a function is increasing?

Back

An increasing interval can be expressed in interval notation, e.g., (a, b) where f(x) is increasing.

Front

What is the notation for a function that is constant between two points?

Back

The notation is typically [a, b] where f(x) remains the same for all x in that interval.