Vertical Line Test

Front

What is the Vertical Line Test?

Back

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

Front

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

Back

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

Front

What is an example of a function?

Back

An example of a function is the graph of y = x^2, where each x-value corresponds to one unique y-value.

Front

What is an example of a non-function?

Back

An example of a non-function is the graph of a circle, such as x^2 + y^2 = r^2, where some x-values correspond to multiple y-values.

Front

How can you determine if a graph is a function using the Vertical Line Test?

Back

To use the Vertical Line Test, draw vertical lines through the graph. If any vertical line crosses the graph at more than one point, it is not a function.

Front

What is the significance of the Vertical Line Test in mathematics?

Back

The Vertical Line Test helps to visually identify functions, making it easier to understand the relationship between variables.

Front

Can a horizontal line test determine if a graph is a function?

Back

No, the horizontal line test determines if a function is one-to-one, not if it is a function.

Front

What is the difference between a function and a relation?

Back

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

Front

What type of graph is guaranteed to be a function?

Back

Linear graphs, such as y = mx + b, are guaranteed to be functions because they pass the Vertical Line Test.

Front

What type of graph is guaranteed to NOT be a function?

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Graphs that are parabolas opening sideways, such as x = y^2, are guaranteed to not be functions because they fail the Vertical Line Test.