Math  /  Geometry

QuestionComplete the sentence below. A set of points in the xy-plane is the graph of a function if and only if every \qquad line intersects the graph in at most one point.
A set of points in the xy-plane is the graph of a function if and only if every \square line intersects the graph in at most one point.

Studdy Solution

STEP 1

1. We are dealing with the definition of a function in terms of its graph.
2. The question is about a specific type of line that tests whether a set of points represents a function.

STEP 2

1. Recall the definition of a function in terms of its graph.
2. Identify the type of line that tests this definition.
3. Complete the sentence using the identified line.

STEP 3

Recall the definition of a function in terms of its graph: A set of points in the xy-plane is the graph of a function if and only if for each input (x-value), there is exactly one output (y-value).

STEP 4

Identify the type of line that tests this definition: This is known as the "Vertical Line Test." A set of points is the graph of a function if and only if no vertical line intersects the graph at more than one point.

STEP 5

Complete the sentence using the identified line: A set of points in the xy-plane is the graph of a function if and only if every vertical line intersects the graph in at most one point.
The completed sentence is:
A set of points in the xy-plane is the graph of a function if and only if every \textbf{vertical} line intersects the graph in at most one point.

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