Determine if Function

Front

What is a function?

Back

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

Front

How can you determine if a graph represents a function?

Back

Use the Vertical Line Test: If a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the Vertical Line Test?

Back

A method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

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

Back

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

Front

Is the graph of y = √x a function?

Back

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

Front

Is the graph of y = ±√x a function?

Back

No, it is not a function because each positive x-value has two corresponding y-values.

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 produced by exactly one input.

Front

Can a function have the same output for different inputs?

Back

Yes, but it cannot have the same input for different outputs.

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.