Proportional vs. Non-Proportional & Functions

Front

What is a function?

Back

A function is a relation in which each input (x-value) is associated with exactly one output (y-value).

Front

What is the definition of a non-function?

Back

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

Front

What is the constant of proportionality?

Back

The constant of proportionality is the ratio between two proportional quantities, often represented as the slope in a linear function.

Front

How do you determine if a relation is a function using a mapping diagram?

Back

A relation is a function if every input (x-value) has only one output (y-value) in the mapping diagram.

Front

What does it mean for a function to be proportional?

Back

A function is proportional if it can be expressed in the form y = kx, where k is a constant.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What is the difference between proportional and non-proportional relationships?

Back

Proportional relationships pass through the origin and have a constant ratio, while non-proportional relationships do not pass through the origin and have varying ratios.

Front

How can you identify a non-proportional function from its equation?

Back

A non-proportional function will have a y-intercept that is not zero, indicating it does not pass through the origin.

Front

What is the equation of a proportional relationship?

Back

The equation of a proportional relationship is typically in the form y = kx, where k is the constant of proportionality.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.