Review: Increasing and Decreasing

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

Define the term 'x-intercept'.

Back

The x-intercept of a graph is the point where the graph crosses the x-axis, meaning the value of y is zero at that point.

Front

What is an interval in mathematics?

Back

An interval is a range of numbers between two endpoints, which can be open (not including endpoints) or closed (including endpoints).

Front

Back

This notation represents all real numbers less than or equal to 0, including 0.

Front

How do you determine the increasing interval of a function from its graph?

Back

To determine the increasing interval, look for sections of the graph where the function rises as you move from left to right.

Front

Back

This notation represents all real numbers greater than or equal to 0.

Front

What is a constant function?

Back

A constant function is a function that does not change its value; it remains the same for all inputs.

Front

How can you identify a constant interval on a graph?

Back

A constant interval on a graph is identified where the graph is horizontal, indicating that the function's value does not change.

Front

What is the significance of the x-intercept in a function?

Back

The x-intercept indicates the value of x at which the function equals zero, which can be important for solving equations.