Function or Not?

Front

What is a function?

Back

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

Front

How can you tell 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 Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

What does it mean if a relation is not a function?

Back

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

Front

Given the relation {(1,5),(1,7),(3,9),(4,11)}, is it a function?

Back

No, it is not a function because the x-value '1' is associated with two different y-values (5 and 7).

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 and may include curves, parabolas, or other shapes.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point on a graph, where 'x' is the input and 'y' is the output.

Front

Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, as long as each x-value corresponds to only one y-value.

Front

What is the definition of a relation in mathematics?

Back

A relation is a set of ordered pairs, which can show how two sets of values are connected.