Function/Not a Function & Linear/Nonlinear

Front

What is a function?

Back

A relation where each input (x) has exactly one output (y).

Front

What is a relation that is NOT a function?

Back

A relation where at least one input (x) has more than one output (y).

Front

How can you determine if a relation is a function using the vertical line test?

Back

If a vertical line intersects the graph of the relation at more than one point, it is NOT a function.

Front

What is a linear function?

Back

A function that graphs to a straight line, represented by the equation y = mx + b.

Front

What is a nonlinear function?

Back

A function that does not graph to a straight line, such as quadratic or exponential functions.

Front

What is the definition of ordered pairs?

Back

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

Front

What does it mean for y to be a function of x?

Back

For every value of x, there is exactly one corresponding value of y.

Front

Give an example of a function using ordered pairs.

Back

{(1, 2), (2, 3), (3, 4)} - Each x-value has one unique y-value.

Front

Give an example of a relation that is NOT a function using ordered pairs.

Back

{(1, 2), (1, 3), (2, 4)} - The x-value 1 has two different y-values.

Front

What is the slope of a linear function?

Back

The slope (m) represents the rate of change of y with respect to x.