Identifying 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 is a function? {(1,2), (2,3), (3,4), (1,5)}

Back

Not a function, because the input 1 has two outputs (2 and 5).

Front

Identify if this set is a function: {(2,3), (3,4), (4,5), (2,6)}

Back

Not a function, because the input 2 has two outputs (3 and 6).

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 {(5,1), (5,2), (6,3)} a function?

Back

No, because the input 5 has two outputs (1 and 2).

Front

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

Back

A one-to-one function is a function where each output is paired with exactly one input, meaning no two different inputs have the same output.

Front

Example of a function: f(x) = 2x + 3. What is f(2)?

Back

f(2) = 2(2) + 3 = 7.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

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

Back

Yes, it is a function because each x-value has only one corresponding y-value.