Functions and Proportional Relationships

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant.

Front

What does it mean if a graph does not touch the origin?

Back

If a graph does not touch the origin, it indicates that the relationship is non-proportional.

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 function?

Back

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

Front

What is a non-function?

Back

A non-function is a relation where at least one input (x-value) has more than one output (y-value).

Front

How can you tell if a relationship is proportional from a table of values?

Back

A relationship is proportional if the ratio of y to x is constant for all pairs of values.

Front

What does it mean for a graph to show a proportional relationship?

Back

A graph shows a proportional relationship if it is a straight line that passes through the origin.

Front

What is the significance of the slope in a proportional relationship?

Back

In a proportional relationship, the slope represents the constant ratio between the two quantities.

Front

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

Back

An example of a proportional relationship is the relationship between distance and time when traveling at a constant speed.

Front

What is an example of a non-proportional relationship?

Back

An example of a non-proportional relationship is the relationship between the number of items purchased and the total cost when there is a fixed fee added.