Function Increasing & Decreasing

Front

What is an increasing function?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, where x1 < x2, the function value at x1 is less than the function value at x2 (f(x1) < f(x2)).

Front

What is a decreasing function?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, where x1 < x2, the function value at x1 is greater than the function value at x2 (f(x1) > f(x2)).

Front

What does the y-intercept of a linear function represent?

Back

The y-intercept is the value of y when x = 0, representing the starting point of the function on the y-axis.

Front

How can you determine if a function is increasing or decreasing from its graph?

Back

If the graph rises as you move from left to right, the function is increasing. If it falls, the function is decreasing.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions have variable rates of change and graph as curves.

Front

What does it mean for a function to be constant?

Back

A function is constant if its value does not change regardless of the input; it graphs as a horizontal line.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function; a positive slope means the function is increasing, while a negative slope means it is decreasing.

Front

What is an interval in the context of functions?

Back

An interval is a range of x-values over which a function is analyzed for increasing or decreasing behavior.

Front

How do you find the intervals where a function is increasing or decreasing?

Back

To find intervals, calculate the derivative of the function and determine where it is positive (increasing) or negative (decreasing).

Front

What does it mean for a function to never decrease?

Back

A function that never decreases is always either increasing or constant; it does not drop in value at any point.