Vertical Line Test

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method used to determine if a curve is a function. If any vertical line intersects the curve at more than one point, the curve is not a function.

Front

What does it mean for a relation to be a function?

Back

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

Front

How can you visually determine if a graph represents a function?

Back

You can visually determine if a graph represents a function by using the Vertical Line Test. If a vertical line crosses the graph more than once, it is not a function.

Front

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

Back

An example of a relation that is not a function is the circle defined by the equation x^2 + y^2 = r^2, as vertical lines can intersect the circle at two points.

Front

What is the significance of the x-value in a function?

Back

In a function, each x-value must correspond to only one y-value, ensuring that the function passes the Vertical Line Test.

Front

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input. This would violate the definition of a function.

Front

What type of graph is guaranteed to be a function?

Back

A straight line with a non-vertical slope is guaranteed to be a function, as it will pass the Vertical Line Test.

Front

What is a common misconception about functions?

Back

A common misconception is that any relation is a function. In reality, a relation must meet the criteria of having only one output for each input.

Front

How does the concept of domain relate to functions?

Back

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

Front

What is the range of a function?

Back

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