Determining Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line. Its rate of change is not constant.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, it is not a function.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be represented by a linear equation and its graph is a straight line.

Front

What does it mean for a function to be nonlinear?

Back

A function is nonlinear if it cannot be represented by a linear equation and its graph is not a straight line.

Front

What is the slope of a linear function?

Back

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

Front

What is the y-intercept of a linear function?

Back

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

Front

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input. Each input must correspond to exactly one output.