Calculus Lecture Information at Sphinx University
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Questions and Answers

Which of the following best describes an even function?

  • A function where $f(x) = -f(x + 2)$ for all $x$ in the domain
  • A function where $f(x) = -f(-x)$ for all $x$ in the domain
  • A function where $f(x) = f(x + 2)$ for all $x$ in the domain
  • A function where $f(x) = f(-x)$ for all $x$ in the domain (correct)

    • What type of function is characterized by the property $g(-x) = -g(x)$ for all $x$ in the domain?

  • Even function
  • Odd function (correct)
  • Neither even nor odd function
  • Increasing function

    • In the context of functions, what does it mean for a function to be increasing?

  • The function has a decreasing trend throughout its domain
  • The slope of the function is zero at all points
  • The function is concave up in its entire domain
  • The function's output increases as its input increases (correct)

    • Which of these statements best describes a decreasing function?

    <p>The function's output decreases as its input decreases</p> Signup and view all the answers

    What is the defining characteristic of a neither even nor odd function?

    <p>The function has no symmetry about the x-axis or y-axis</p> Signup and view all the answers

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