Direct Variation/Constant of Variation and a few functions

Front

What is Direct Variation?

Back

Direct Variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed in the form y = kx, where k is the constant of variation.

Front

What does the constant of variation represent?

Back

The constant of variation (k) represents the ratio of the two variables in a direct variation. It indicates how much one variable changes in relation to the other.

Front

If y = 5x, what is the constant of variation?

Back

The constant of variation is 5.

Front

How can you determine if a relationship is a direct variation?

Back

A relationship is a direct variation if it can be expressed in the form y = kx, and the ratio y/x is constant.

Front

What is an example of a direct variation?

Back

An example of direct variation is the relationship between distance and time when speed is constant: d = rt, where r is the speed.

Front

What is a function?

Back

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

Front

Does the mapping {(1,2), (2,3), (3,4)} represent a function?

Back

Yes, because each input has a unique output.

Front

Does the mapping {(1,2), (1,3), (2,4)} represent a function?

Back

No, because the input 1 has two different outputs (2 and 3).

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point in a coordinate system.

Front

What does it mean if a table does not represent a function?

Back

It means that at least one input corresponds to more than one output.