Understand Functions

Front

What is a function?

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 tell if a relation is a function?

Back

A relation is a function if every 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 curve is a function. If a vertical line intersects the curve at more than one point, it is not a function.

Front

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

Back

For a set of ordered pairs to be a function, no two pairs can have the same first element (x-value) with different second elements (y-values).

Front

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

Back

No, because the input '1' is associated with two different outputs (2 and 4).

Front

Is the set {(3, 5), (4, 5), (5, 5)} a function?

Back

Yes, because each input has exactly one output.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with an output.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

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

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.