Identifying 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

Does this table depict a function? (Example: x: 1, 2, 3; y: 4, 5, 6)

Back

Yes, each input (x) has a unique output (y).

Front

Does this table depict a function? (Example: x: 1, 2, 2; y: 3, 4, 5)

Back

No, the input '2' has two different outputs (4 and 5).

Front

Is height a function of age? (Example: Age: 5, 6, 7; Height: 3, 4, 5)

Back

No, height can vary for the same age.

Front

Is time a function of distance? (Example: Distance: 1 mile, 2 miles; Time: 10 min, 20 min)

Back

No, time can vary based on speed.

Front

What is the vertical line test?

Back

A method to determine if a curve is a function; if a vertical line crosses the graph more than once, it is not a function.

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.

Front

What is an example of a function in real life?

Back

The relationship between the temperature in Celsius and Fahrenheit is a function.

Front

What is a non-function example?

Back

A relationship where one input corresponds to multiple outputs, like a person's name and their phone numbers.

Front

What does it mean for a relation to be one-to-one?

Back

A one-to-one relation means that each input has a unique output and no two inputs share the same output.