IS IT A FUNCTION?

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 determines 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

Is the set of points {(1,2), (2,3), (1,4)} a function?

Back

No, it is not a function because the input '1' has two different outputs (2 and 4).

Front

Is the mapping {(1,2), (2,3), (3,4)} a function?

Back

Yes, it is a function because each input has exactly one output.

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 is associated with more than one output.

Front

Can a vertical line ever represent a function?

Back

No, a vertical line represents a relation where every x-value has the same y-value, which does not satisfy the definition of a function.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique y-value.

Front

What is an example of a relation that is not a function?

Back

An example is the relation defined by the equation x^2 + y^2 = 1, which fails the vertical line test.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents the relationship between inputs and outputs, helping to determine if a relation is a function.