Linear and Nonlinear Functions

Front

What is a function?

Back

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

Front

What is the vertical line test?

Back

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

Front

What is the horizontal line test?

Back

The horizontal line test is used to determine if a function is one-to-one. If a horizontal line intersects the graph at more than one point, the function is not one-to-one.

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 graph can be a curve, a circle, or any other shape that is not linear.

Front

Can a vertical line be a function?

Back

No, a vertical line represents a relation where each x-value corresponds to multiple y-values, which violates the definition of a function.

Front

What does it mean for a relation to be not a function?

Back

A relation is not a function if at least one input (x-value) corresponds to more than one output (y-value).

Front

How can you tell if a table represents a function?

Back

A table represents a function if each x-value is unique and does not repeat with different y-values.

Front

What is the slope of a linear function?

Back

The slope of a linear function (m) represents the rate of change of y with respect to x. It indicates how steep the line is.

Front

What is the y-intercept of a linear function?

Back

The y-intercept (b) is the point where the graph of the function crosses the y-axis, represented as (0, b).