Functions (general)

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the rate of change in a function?

Back

The rate of change is a measure of how a quantity changes in relation to another quantity, often represented as the slope of a line connecting two points on a graph.

Front

How do you calculate the rate of change between two points (x1, y1) and (x2, y2)?

Back

Front

What does a positive rate of change indicate?

Back

A positive rate of change indicates that as the input increases, the output also increases.

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that as the input increases, the output decreases.

Front

What is the average rate of change over an interval?

Back

The average rate of change over an interval is calculated by dividing the change in the output by the change in the input over that interval.

Front

If a function has a constant rate of change, what type of function is it?

Back

It is a linear function.

Front

What is the slope of a line?

Back

The slope of a line is the ratio of the vertical change to the horizontal change between two points on the line.

Front

How do you express a slope as a fraction?

Back

Front

What is the significance of an undefined slope?

Back

An undefined slope occurs when the line is vertical, indicating that there is no change in the x-values.