Identifying Functions Through Various Representations

What defines a function in terms of input and output?

• Each input can have multiple outputs

• There are no restrictions on inputs and outputs

• Each input has exactly one output

• Each output can have multiple inputs

What does the vertical line test determine?

• If a graph represents a non-linear function

• If a graph represents a function based on intersections

• If a graph represents a function based on x-values

• If a graph represents a continuous function

Why is a relation with repeating x-values not considered a function?

• Because it cannot be graphed

• Because it is not a mathematical relation

• Because each input does not have a unique output

• Because it fails the vertical line test

What outcome in the vertical line test indicates that a graph is not a function?

• The line intersects the graph at multiple points

• The line runs parallel to the graph

• The line intersects the graph at exactly one point

• The line does not touch the graph

In a graph, what does an open circle indicate?

• The point is included in the function

• The point is not included in the function

• The function is discontinuous at that point

• The function has an undefined slope at that point

How does a closed circle on a graph affect the vertical line test?

• It makes the graph linear

• It indicates the point is included, potentially failing the test

• It has no effect on the vertical line test

• It indicates the graph is always a function

What does a mapping need to show to be considered a function?

• No inputs are connected to outputs

• Each input is connected to exactly one output

• Each output is connected to exactly one input

• Each input is paired with at least two outputs

What does the presence of multiple outputs for a single input imply about a relation?

• It is not a function

• It is definitely a function

• It could be a function depending on the graph type

• It only applies to linear functions

Why does a vertical line graph not pass the vertical line test?

• Because it is parallel to the y-axis

• Because it intersects the graph at only one point

• Because it does not intersect the graph

• Because it intersects the graph at multiple points

How does a horizontal line perform in the vertical line test?

• It passes because it is parallel to the x-axis

• It passes because it intersects at exactly one point

• It fails because it intersects at multiple points

• It fails because it does not intersect