Unit 1, Lesson 1: Exploring Relations
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Questions and Answers

What should be written if the input x is odd?

  • 1 (correct)
  • 0
  • x
  • y

    • What does the mapping diagram represent when using the rule 'divide by 4, and then add 2'?

  • The difference between the inputs
  • Input-output pairs of a relation (correct)
  • The sum of the inputs
  • The average of the outputs

    • If the input is -8 in the given mapping diagram, what is the output?

  • 8
  • 2
  • 4 (correct)
  • 0

    • When input 1 is processed in the mapping diagram, what output is produced?

    <p>0</p> Signup and view all the answers

    Which of the following statements is true regarding even inputs?

    <p>They should yield an output of 0.</p> Signup and view all the answers

    What is the output when the input is 6 in this mapping relation?

    <p>2</p> Signup and view all the answers

    How are inputs and outputs represented in a mapping diagram?

    <p>By arrows connecting each pair</p> Signup and view all the answers

    What is the relationship between inputs and outputs in a relation?

    <p>Each output corresponds to no more than one input.</p> Signup and view all the answers

    What is the range of Relation A based on the given mapping diagram?

    <p>{-5, -2, 1, 2, 3, 4, 5}</p> Signup and view all the answers

    Which of the following points does NOT belong to Relation B?

    <p>(1, 3)</p> Signup and view all the answers

    For Relation A, which y-value corresponds to the x-value of 1?

    <p>2</p> Signup and view all the answers

    What is the domain of Relation B?

    <p>{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}</p> Signup and view all the answers

    Which statement is true regarding the relationship between Relation A and Relation B?

    <p>Relation A has a greater range than Relation B.</p> Signup and view all the answers

    Identify the incorrect mapping for Relation A.

    <p>(0, 3)</p> Signup and view all the answers

    What value of y corresponds to the x-value of -4 in Relation B?

    <p>-1</p> Signup and view all the answers

    Which of these x-values has the highest y-value in Relation A?

    <p>5</p> Signup and view all the answers

    What is the input-output rule that results in an output of $-15$ when the input is $-5$?

    <p>Add 10 and then multiply by 3</p> Signup and view all the answers

    If an input value is $2.5$, what would be the resulting output using the rule of adding 10 and dividing by 3?

    <p>4.17</p> Signup and view all the answers

    Which of the following outputs corresponds to the input value of $6$ with the rule of multiplying by 3?

    <p>18</p> Signup and view all the answers

    What will be the output if the input value is $3$ after applying the rule of adding 1 and then multiplying by 4?

    <p>10</p> Signup and view all the answers

    If you take an input of $4$ and apply the rule of adding 1 and multiplying by 4, what changes to the output result would you expect?

    <p>It increases significantly</p> Signup and view all the answers

    Which output corresponds to an input of $0$ using the input-output rule of multiplying by 3?

    <p>0</p> Signup and view all the answers

    If the output is $7.5$, what could be a possible input if using the rule of adding 10 and dividing by 3?

    <p>0</p> Signup and view all the answers

    What is a suitable output for an input of $-1$ under the rule of multiplying by 3?

    <p>-3</p> Signup and view all the answers

    What would the output be for an input of 16 in the function that finds the square root of the input?

    <p>2</p> Signup and view all the answers

    Which of the following statements accurately describes the inputs and outputs in a relation?

    <p>Outputs are dependent variables and inputs are independent variables.</p> Signup and view all the answers

    For an input value of -2 in the function that subtracts 3 and multiplies by 12, what is the output?

    <p>-12</p> Signup and view all the answers

    What can be inferred about the relationship between input values and outputs from the context provided?

    <p>The output values depend directly on the input values.</p> Signup and view all the answers

    In the mapping diagram, which input value results in an output of –4?

    <p>-4</p> Signup and view all the answers

    What happens to the input of 0 in the square root function?

    <p>Yields zero.</p> Signup and view all the answers

    What is the effect of subtracting 3 from the input before multiplying by 12 in terms of changes to the output?

    <p>It can result in a negative output value.</p> Signup and view all the answers

    If inputs are represented as x and outputs as y, which of the following options is true based on the relation described?

    <p>For every value of x, there is only one value of y.</p> Signup and view all the answers

    What does the mapping diagram represent in relation to the graph?

    <p>Direct comparison of points to arrows.</p> Signup and view all the answers

    In a relation, which variable represents the set of input values?

    <p>Independent variable</p> Signup and view all the answers

    Which of the following correctly describes the relationship between ordered pairs and mapping diagrams?

    <p>Mapping diagrams can represent any ordered pairs.</p> Signup and view all the answers

    How many input-output pairs does the mapping diagram for each relation have?

    <p>Three or more</p> Signup and view all the answers

    What is the significance of the input value from the mapping diagram in relation to the graph?

    <p>It matches the x-value of the point on the graph.</p> Signup and view all the answers

    Which of the following represents the output values in the ordered pairs of a relation?

    <p>The second element of each pair</p> Signup and view all the answers

    What can be said about the number of points on the graph that corresponds to the mapping diagram?

    <p>It is always equal to the number of input-output pairs.</p> Signup and view all the answers

    Which of the following formats can represent a relation?

    <p>Through tables, graphs, mapping diagrams, or sets of ordered pairs.</p> Signup and view all the answers

    Study Notes

    Understanding Relations

    • A relation is defined as a set of input-output pairs.
    • Input-output rules use input values to determine corresponding output values.

    Input-Output Rules

    • An example rule takes an input, applies a mathematical operation, and results in an output.
    • For example, input of -5 yields an output of -15 by applying a specific rule.

    Collaborative Activities

    • Partner activities involve identifying rules and completing input-output tables based on various mathematical operations.
    • Rules can include adding or subtracting constants, as well as multiplying or dividing values.

    Mapping Diagrams

    • Relations can also be represented using mapping diagrams, which visually display how inputs are connected to outputs through arrows.
    • Each input corresponds to exactly one output in a mapping diagram.

    Graphical Representation

    • Each relation can be illustrated using graphs, where points represent input-output pairs.
    • The graph directly reflects the relationships shown in the mapping diagram.

    Terminology in Relations

    • Inputs are considered independent variables, while outputs are dependent variables.
    • A graph represents the set of ordered pairs, linking x-values (inputs) to y-values (outputs).

    Comparing Representations

    • Observations can be made by comparing mapping diagrams and graphs for insights into input-output relationships.
    • Each representation (table, mapping, graph, ordered pairs) provides a different visual or mathematical insight into the same relation.

    Additional Notes

    • The ability to recognize relations in multiple forms is a vital skill in understanding foundational mathematical concepts.
    • Complete practice activities in pairs to reinforce understanding of input-output rules and their representations.

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    U1L1 Exploring Relations PDF

    Description

    This quiz focuses on recognizing and representing mathematical relations in different forms. Students will explore input-output rules through collaborative activities, enhancing their understanding of how values relate to one another. Test your knowledge of the concepts introduced in this lesson!

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