Direct Variation and Functions

Front

What is the definition of a function?

Back

A function is a relation where every input has only ONE output.

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other.

Front

Is the equation y = 3x a direct variation?

Back

Yes, because it can be expressed in the form y = kx, where k is a constant (k=3).

Front

Is the equation y = x^2 a direct variation?

Back

No, because it does not have the form y = kx.

Front

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

Back

A relation is a function if each input is associated with exactly one output.

Front

What is an example of a function?

Back

The equation y = 2x + 1 is a function.

Front

What is an example of a relation that is not a function?

Back

The relation {(1, 2), (1, 3)} is not a function because the input 1 has two different outputs.

Front

How can you determine if a set of points represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the slope in a direct variation equation?

Back

The slope is the constant of variation (k) in the equation y = kx.

Front

If y varies directly with x, and y = 10 when x = 2, what is the constant of variation?

Back

The constant of variation k is 5, since k = y/x = 10/2.