Functions and Graphs
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Questions and Answers

What is the formula to calculate the gradient of a line?

  • $\frac{y_2 - y_1}{x_2 - x_1}$ (correct)
  • $\frac{x_2 - x_1}{y_2 - y_1}$
  • $\frac{x_1 + y_1}{x_2 + y_2}$
  • $\frac{x_2 + x_1}{y_2 + y_1}$

    • Which of the following is NOT a way to represent a relationship between variables?

  • Scatter plot (correct)
  • Verbal description
  • Flow diagram
  • Table

    • What is the term for a quantity that can change?

  • Output number
  • Variable (correct)
  • Function value
  • Input number

    • What is the purpose of interpreting graphs?

    <p>To visualize the relationship between variables</p> Signup and view all the answers

    What is the term for the rate of change between variables in a graph?

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

    Which of the following is a feature to consider when interpreting graphs?

    <p>Shape of the graph</p> Signup and view all the answers

    What is the term for the points where a graph crosses the axes?

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

    What is the purpose of a flow diagram in representing a relationship between variables?

    <p>To show the calculations needed to transform input into output</p> Signup and view all the answers

    What is the term for the result after applying a function to an input?

    <p>Function value</p> Signup and view all the answers

    Which of the following is a type of representation of a relationship between variables?

    <p>All of the above</p> Signup and view all the answers

    Which representation of a relationship between variables is particularly useful for visualizing the relationship between two variables?

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

    What does the gradient of a line passing through two points represent?

    <p>The rate of change between the x and y variables</p> Signup and view all the answers

    Which of the following is a characteristic of a function?

    <p>Each input has exactly one output</p> Signup and view all the answers

    What is the purpose of finding the intercepts of a graph?

    <p>To find the points where the graph crosses the axes</p> Signup and view all the answers

    What is a common use of flow diagrams in representing relationships between variables?

    <p>To show the calculations needed to transform input into output</p> Signup and view all the answers

    What can be inferred about the relationship between variables from the shape of the graph?

    <p>The type of function (linear, quadratic, etc.)</p> Signup and view all the answers

    Which representation of a relationship between variables is particularly useful for identifying patterns and trends?

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

    What is the term for the specific output corresponding to a given input?

    <p>Function value</p> Signup and view all the answers

    Which of the following is a key feature to consider when interpreting graphs?

    <p>The continuity of the graph</p> Signup and view all the answers

    What does the continuity of a graph indicate about the relationship between variables?

    <p>Whether the graph is a continuous line or has breaks/discontinuities</p> Signup and view all the answers

    Study Notes

    Functions, Patterns, and Graphs

    Representations of Relationships

    • Relationships between variables can be represented in multiple ways, including flow diagrams, tables, formulas, verbal descriptions, and graphs.

    Gradient of a Line

    • The gradient (or slope) of a line can be calculated using the formula: Gradient = (y2 - y1) / (x2 - x1)

    Understanding Functions

    • A function describes a relationship between two variables where each input has exactly one output.
    • Functions can be represented in various ways, including:
      • Tables: displaying values of input and corresponding output
      • Flow diagrams: showing the calculations needed to transform input into output
      • Formulas: algebraic expressions that define the function
      • Graphs: visual representations of the function on a coordinate plane

    Key Concepts in Functions

    • A variable is a quantity that can change.
    • An input number is the value substituted into a function.
    • An output number is the result after applying the function to the input.
    • A function value is the specific output corresponding to a given input.

    Interpreting Graphs

    • Graphs provide a visual method to understand the relationship between variables.
    • Key features to consider when interpreting graphs include:
      • Slope/Gradient: indicates the rate of change between variables
      • Intercepts: points where the graph crosses the axes
      • Continuity: whether the graph is a continuous line or has breaks/discontinuities
      • Shape of the Graph: linear, quadratic, exponential, etc., which provides insights into the nature of the relationship

    Functions, Patterns, and Graphs

    Representations of Relationships

    • Relationships between variables can be represented in multiple ways, including flow diagrams, tables, formulas, verbal descriptions, and graphs.

    Gradient of a Line

    • The gradient (or slope) of a line can be calculated using the formula: Gradient = (y2 - y1) / (x2 - x1)

    Understanding Functions

    • A function describes a relationship between two variables where each input has exactly one output.
    • Functions can be represented in various ways, including:
      • Tables: displaying values of input and corresponding output
      • Flow diagrams: showing the calculations needed to transform input into output
      • Formulas: algebraic expressions that define the function
      • Graphs: visual representations of the function on a coordinate plane

    Key Concepts in Functions

    • A variable is a quantity that can change.
    • An input number is the value substituted into a function.
    • An output number is the result after applying the function to the input.
    • A function value is the specific output corresponding to a given input.

    Interpreting Graphs

    • Graphs provide a visual method to understand the relationship between variables.
    • Key features to consider when interpreting graphs include:
      • Slope/Gradient: indicates the rate of change between variables
      • Intercepts: points where the graph crosses the axes
      • Continuity: whether the graph is a continuous line or has breaks/discontinuities
      • Shape of the Graph: linear, quadratic, exponential, etc., which provides insights into the nature of the relationship

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    Description

    This quiz covers the basics of functions, patterns, and graphs, including representations of relationships, gradient of a line, and understanding functions.

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