8.F.1-Function or Not 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 definition of 'not a function'?

Back

A relation is not a function if at least one input (x-value) has more than one output (y-value).

Front

Example of a function: y = 2x + 3. Is this a function?

Back

Yes, this is a function because for every x-value, there is exactly one y-value.

Front

Example of a relation that is not a function: {(1, 2), (1, 3)}. Is this a function?

Back

No, this is not a function because the input 1 has two different outputs (2 and 3).

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

If a relation has the pairs (2, 4), (3, 5), (2, 6), is it a function?

Back

No, it is not a function because the input 2 has two outputs (4 and 6).

Front

What does the term 'domain' refer to in functions?

Back

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

Front

What does the term 'range' refer to in functions?

Back

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

Is the equation y = x^2 a function?

Back

Yes, y = x^2 is a function because each x-value has exactly one corresponding y-value.