Identifying Functions and Relations

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Questions and Answers

What does the vertical line test determine about a graph?

  • Whether the graph represents a function. (correct)
  • Whether the graph has a maximum or minimum value.
  • Whether the graph is continuous.
  • Whether the graph intersects the x-axis.

In the given relation, which x-value indicates the presence of multiple y-values?

  • -7
  • 8
  • 11 (correct)
  • 3

If a relation has the pair (5, 8) as part of its input-output pairs, which of the following could invalidate it as a function?

  • (5, 10) (correct)
  • (3, 5)
  • (7, 8)
  • (5, 12) (correct)

What condition must be met for a relation to be classified as a function?

<p>Every x-value must have a unique output y-value. (A)</p>
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If a graph fails the vertical line test, what can be concluded about it?

<p>It cannot be classified as a function. (A)</p>
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Based on the table provided, why is it classified as not a function?

<p>There are repeated x-values with different y-values. (A), Outputs are not unique to the inputs. (C)</p>
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In the mapping diagram, which of the following statements accurately describes why it is not a function?

<p>At least one input is mapped to multiple outputs. (C)</p>
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What characteristic must hold true for a relation to be defined as a function?

<p>Every input must have only one associated output. (C)</p>
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Which of the following could potentially result in a relation being not a function?

<p>Repeating x-values with different y-values. (A)</p>
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In the context of functions, which definition is accurate?

<p>A function relates inputs to outputs uniquely. (A)</p>
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Which of the following best defines the domain of a function?

<p>The set of all input values (B)</p>
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What does the range of a function specifically refer to?

<p>All possible y-values (B)</p>
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In a mapping diagram, what is typically shown by the lines connecting the ovals?

<p>The relationship between input and output (A)</p>
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Which of the following statements is true regarding the vertical line test?

<p>It checks if a relation is a function (D)</p>
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If a function does not pass the vertical line test, what can be concluded?

<p>It is not a function (D)</p>
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How can the relationship between the numbers in the ovals be interpreted?

<p>As a mapping relation (C)</p>
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Which option best describes the term 'mapping' in mathematics?

<p>A representation of functions through ordered pairs (A)</p>
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Considering the possible sets of values, which pair would typically not be included in a mapping diagram?

<p>Input-value of 5 to output-value of 5 and 6 (D)</p>
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Flashcards

Function?

A relation where every input has exactly one output. No input can have multiple outputs.

Function test: Table

Examine the table to see if any input (X) values are linked to multiple output (Y) values. If so, it's not a function.

Function test: Mapping Diagram

Check if any input (arrow source) has more than one output (arrow destination). If so, it's not a function.

Function definition

A function is a mathematical rule where every input value maps to exactly one output value.

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Vertical Line Test

A test used to determine if a graph represents a function. A graph represents a function if and only if no vertical line intersects the graph at more than one point.

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Function rule

A function is defined by the rule that links each input to its unique output.

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Relation

A set of ordered pairs (x, y) that shows a connection between inputs and outputs.

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Repeating Input Values

When the same input value (x-value) has multiple output values (y-values).

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Function Test

Checking if a graph or relation meets the rules of a function. This involves ensuring that each input has only one output.

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Domain

The set of all possible input values (x-values) for a function or relation.

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Range

The set of all possible output values (y-values) for a function or relation.

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Mapping

A visual representation of a relation that shows how each input value (x-value) is paired with an output value (y-value).

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Graph

A visual representation of a relation where points are plotted on a coordinate plane.

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Not a Function

A relation where at least one input value (x-value) is paired with more than one output value (y-value).

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Study Notes

Graph representing a function

  • The graph does not represent a function because the vertical line test shows repeating input values

Relation as a function

  • The relation is not a function because the x-value 11 has two y-values paired with it.

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