Functions and Proportional Relationships

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio, meaning as one quantity increases, the other increases at a consistent rate.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant, often represented by a line that does not pass through the origin.

Front

What does it mean for a graph to pass the vertical line test?

Back

A graph passes the vertical line test if no vertical line intersects the graph at more than one point, indicating that each input (x-value) has only one output (y-value).

Front

What is a function?

Back

A function is a relation where each input has exactly one output.

Front

What is an example of a non-function?

Back

A relation where an input corresponds to multiple outputs, such as a vertical line or a mapping where one x-value is paired with two different y-values.

Front

What is the significance of the origin in proportional relationships?

Back

In proportional relationships, the graph passes through the origin (0,0), indicating that when one quantity is zero, the other is also zero.

Front

How can you determine if a table of values represents a proportional relationship?

Back

A table represents a proportional relationship if the ratios of corresponding values are constant.

Front

What does it mean if a graph is described as proportional?

Back

A proportional graph is a straight line that passes through the origin, indicating a constant rate of change.

Front

What is the slope of a proportional relationship?

Back

The slope of a proportional relationship is the constant ratio of the change in y to the change in x, often represented as 'k' in the equation y = kx.

Front

What is an example of a proportional relationship in real life?

Back

An example is earning money at a constant hourly rate, such as $10 per hour, where the total earnings are directly proportional to the hours worked.