Increasing and Decreasing Functions

Front

What is an increasing function?

Back

A function is increasing if, for any two points x1 and x2 in its domain, if x1 < x2, then f(x1) < f(x2).

Front

What is a decreasing function?

Back

A function is decreasing if, for any two points x1 and x2 in its domain, if x1 < x2, then f(x1) > f(x2).

Front

What does a positive slope indicate about a function?

Back

A positive slope indicates that the function is increasing.

Front

What does a negative slope indicate about a function?

Back

A negative slope indicates that the function is decreasing.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line and can have curves or bends.

Front

How can you identify an increasing function on a graph?

Back

An increasing function on a graph rises from left to right.

Front

How can you identify a decreasing function on a graph?

Back

A decreasing function on a graph falls from left to right.

Front

What is the slope of a constant function?

Back

The slope of a constant function is zero.

Front

What does it mean if a function is never decreasing?

Back

If a function is never decreasing, it means that it is either increasing or constant throughout its domain.