Continuous vs discrete and linear vs non linear

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, indicating a constant rate of change.

Front

What is a non-linear function?

Back

A non-linear function is a function that does not graph to a straight line, indicating a variable rate of change.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is a discrete function?

Back

A discrete function is a function that consists of distinct, separate values, often represented as individual points.

Front

What is a continuous function?

Back

A continuous function is a function that can be graphed with a single unbroken line, meaning it has no gaps or jumps.

Front

Give an example of a linear function.

Back

An example of a linear function is f(x) = 2x + 3.

Front

Give an example of a non-linear function.

Back

An example of a non-linear function is f(x) = x^2.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the rise (change in y) to the run (change in x), indicating the steepness of the line.

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as the x-values increase, the y-values also increase.