Functions!

Front

What is a function in mathematics?

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

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is the difference between a linear function and a nonlinear function?

Back

A linear function has a constant rate of change and can be represented by a straight line, while a nonlinear function does not have a constant rate of change and can be represented by curves.

Front

What is an ordered pair in the context of functions?

Back

An ordered pair is a pair of numbers (x, y) that represents a point in a coordinate system, where 'x' is the input and 'y' is the output.

Front

What does it mean for a set of ordered pairs to be a function?

Back

A set of ordered pairs is a function if no two different ordered pairs have the same first element (input).

Front

What is the definition of a linear function?

Back

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

Front

What is the definition of a nonlinear function?

Back

A nonlinear function is a function that cannot be expressed in the form y = mx + b and may include quadratic, exponential, or other types of relationships.

Front

What is the significance of the slope in a linear function?

Back

The slope of a linear function indicates the rate of change of the function; it represents how much 'y' changes for a unit change in 'x'.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of 'y' when 'x' is 0.

Front

How can you identify a nonlinear function from a set of ordered pairs?

Back

A nonlinear function can be identified if the change in 'y' values does not remain constant for equal changes in 'x' values.