Function or Not a Function?

Front

What is a function in mathematical terms?

Back

A function is a relation where each 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 graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What does it mean for a graph to pass the vertical line test?

Back

A graph passes the vertical line test if any vertical line drawn through the graph intersects it at most once.

Front

Can a function have the same y value for different x values?

Back

Yes, a function can have the same y value for different x values, as long as each x value corresponds to only one y value.

Front

What is an example of a relation that is not a function?

Back

A relation where an x value is paired with multiple y values, such as the equation y^2 = x, is not a function.

Front

What is the definition of a one-to-one function?

Back

A one-to-one function is a function where each x value maps to a unique y value, and each y value is mapped from a unique x value.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has exactly one output, while a relation can have multiple outputs for a single input.

Front

How can you determine if a graph is a function using its equation?

Back

You can determine if a graph is a function by checking if for every x value in the equation, there is only one corresponding y value.

Front

What is a common mistake when identifying functions?

Back

A common mistake is assuming that a relation is a function simply because it has a unique output for some inputs, without checking all inputs.

Front

What is the significance of the domain and range in functions?

Back

The domain is the set of all possible input values (x values) for a function, while the range is the set of all possible output values (y values).