Determining Functions: Key Concepts and Examples

What is the definition of a function in mathematics?

• A rule where each output has exactly one input.

• A rule where each output has multiple inputs.

• A rule where each input has exactly one output.

• A rule where each input has multiple outputs.

Which of the following terms is NOT a synonym for 'input'?

• Range

• Domain

• X value

• Independent variable

In a table, if an X value is paired with more than one Y value, what can be concluded?

• It is a function.

• It is not a function.

• It is a linear function.

• It is a quadratic function.

Given the points (4, 5), (7, 9), (4, -2), is this a function?

• No, because 7 is paired with 9.

• Yes, because the Y values are different.

• No, because 4 is paired with two different Y values.

• Yes, because each X has one Y.

In an arrow diagram, what indicates that a relationship is not a function?

• An X value has multiple arrows pointing to different Y values.

• An X value has no arrows pointing to any Y value.

• Each X value has one arrow pointing to a Y value.

• Each Y value has one arrow pointing to an X value.

In a graph, how can you determine if a relationship is a function?

• If any vertical line intersects the graph at more than one point.

• If any horizontal line intersects the graph at more than one point.

• If the graph is a straight line.

• If the graph is a curve.

Which axis is horizontal in a graph?

• W-axis

• X-axis

• Y-axis

• Z-axis

How can you tell if an equation represents a function?

• If X does not have an exponent.

• If Y has an exponent.

• If Y does not have an exponent.

• If X has an exponent.

In the equation y = 3x + 2, is this a function?

• Yes, because Y has no exponent.

• No, because Y has an exponent.

• Yes, because X has an exponent.

• No, because X has no exponent.

If a table shows the same X value paired with the same Y value multiple times, is it a function?

• No, because X repeats.

• Yes, because Y repeats.

• No, because Y repeats.

• Yes, because each X has one Y.