Relations, Functions, & Linear vs. Nonlinear

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input.

Front

How can you determine if a mapping is a function?

Back

A mapping is a function if every input has exactly one output.

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 origin in a coordinate system?

Back

The origin is the point where the x-axis and y-axis intersect, represented as (0,0).

Front

What distinguishes a linear function from 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 a curve.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, which can include functions but is not limited to them.

Front

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input; this would violate the definition of a function.

Front

What is a linear equation?

Back

A linear equation is an equation that can be written in the form y = mx + b, where m is the slope and b is the y-intercept.