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Algebra 2 - Function Characteristics
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Algebra 2 - Function Characteristics

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Questions and Answers

What is the domain of a function?

  • The maximum point of a graph
  • The set of all possible x-values (correct)
  • The set of all possible y-values
  • The visual representation of a function

    • What is the range of a function?

  • The set of all possible y-values (correct)
  • The relationship between domain and range
  • The set of all possible x-values
  • The minimum point of a graph

    • What is the x-intercept?

    The place where a function crosses or touches the x-axis.

    What is the y-intercept?

    <p>The place where a function crosses or touches the y-axis.</p> Signup and view all the answers

    What defines a function?

    <p>A relationship between two sets where each element of the domain is paired with exactly one element of the range.</p> Signup and view all the answers

    A one-to-one function has each element of the range paired with more than one element of the domain.

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

    What is the vertical line test?

    <p>A test to determine if a relationship is a function by checking if each x has only one y.</p> Signup and view all the answers

    What is the horizontal line test used for?

    <p>To determine if a function is also one-to-one by checking if each y has only one x.</p> Signup and view all the answers

    What is the maximum point on a graph?

    <p>A high point on the graph, visually a 'peak'.</p> Signup and view all the answers

    What is the minimum point on a graph?

    <p>A low point on the graph, visually a 'valley'.</p> Signup and view all the answers

    What is a vertex in the context of functions?

    <p>Either the highest or lowest point on a graph.</p> Signup and view all the answers

    What is a turning point?

    <p>A place where the graph changes direction either from increasing to decreasing or vice versa.</p> Signup and view all the answers

    What is an inflection point?

    <p>A point on the graph where the concavity of the graph is changing.</p> Signup and view all the answers

    What is an increasing interval?

    <p>An x-interval where the function is increasing as x gets bigger.</p> Signup and view all the answers

    What is a decreasing interval?

    <p>An x-interval where the function is decreasing as x gets bigger.</p> Signup and view all the answers

    What is end behavior in functions?

    <p>A description of what the y-values are doing as x approaches either negative or positive infinity.</p> Signup and view all the answers

    Study Notes

    Function Characteristics Vocabulary

    • Domain: All possible x-values for a function.

    • Range: All possible y-values for a function.

    • x-intercept: The point where the function intersects the x-axis, represented as (x, 0).

    • y-intercept: The point where the function intersects the y-axis, represented as (0, y).

    • Function: A relation that pairs each element in the domain with exactly one element in the range, ensuring each x correlates to one y.

    • One-to-one function: A function in which each element of the range corresponds to exactly one element of the domain; every y has a unique x.

    • Vertical Line Test: A visual method used to assess if a relation is a function by checking if each x-value corresponds to only one y-value.

    • Horizontal Line Test: A visual method to determine if a function is one-to-one by checking if each y-value corresponds to only one x-value.

    • Maximum: The highest point of a graph, visually resembling a peak.

    • Minimum: The lowest point of a graph, visually resembling a valley.

    • Vertex: The point on a graph that is either the highest (maximum) or the lowest (minimum) of the function.

    • Turning Point: A point where the graph's direction changes, marking transitions from increasing to decreasing or vice versa; includes maximums and minimums.

    • Inflection Point: A point on the graph where the concavity changes between concave up and concave down.

    • Increasing Interval: An x-interval indicating where the function rises as x increases, represented in the form (x, x).

    • Decreasing Interval: An x-interval indicating where the function falls as x increases, represented in the form (x, x).

    • End behavior: Describes the behavior of y-values as x approaches negative or positive infinity, noted as x → -∞, y → and x → ∞, y → .

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    Description

    Test your knowledge of key vocabulary terms related to functions in Algebra 2. This quiz covers essential concepts like domain, range, and intercepts, providing a solid foundation for understanding function characteristics. Perfect for students looking to reinforce their learning.

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