Representations of Functions

Front

What is a function?

Back

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

Front

Which of the following sets of values is a function? (9,5) (10,5) (9,-5) (10,-5), (3,4) (4,-3) (7,4) (3, 8), (6,-5) (7, -3) (8, -1) (9, 1), (2, -2) (5, 9) (5, -7) (1, 4)

Back

(6,-5) (7, -3) (8, -1) (9, 1) is a function.

Front

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

Back

Not a Function, because the x-value of 1 has two different y-values (2 and 3).

Front

Is the graph of y = x^2 a function?

Back

Function, because for every x-value, there is exactly one y-value.

Front

What is the vertical line test?

Back

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

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

Back

Yes, because each x-value has only one y-value.

Front

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

Back

No, because the x-value of 1 has two y-values (2 and 3).

Front

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

Back

A one-to-one function means that each output is paired with exactly one input, and no two different inputs have the same output.

Front

What is a domain in a function?

Back

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

Front

What is a range in a function?

Back

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