Function Families and Their Properties Quiz

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Questions and Answers

Which function families always have all real numbers for the domain? (Select all that apply)

  • Linear (correct)
  • Exponential (correct)
  • Cube Root (correct)
  • Sine (correct)
  • Cubic (correct)
  • Quadratic

Which function families have all real numbers for the range? (Select all that apply)

  • Cubic (correct)
  • Tangent
  • Log
  • Cube Root (correct)

Which function families may have no x intercepts? (Select all that apply)

  • Exponential (correct)
  • Quadratic
  • Square Root (correct)
  • Rational (correct)
  • Linear

Which function families may have no y intercepts? (Select all that apply)

<p>Log (A), Rational (B)</p> Signup and view all the answers

Which functions have vertical asymptotes? (Select all that apply)

<p>Tangent (A), Log (B), Rational (C)</p> Signup and view all the answers

Which functions have horizontal asymptotes? (Select all that apply)

<p>Exponential (A), Rational (B)</p> Signup and view all the answers

Which functions have defined end behavior for both ends as $x \to \infty$?

<p>Linear, quadratic, cubic, rational, cube root, exponential</p> Signup and view all the answers

Which function family has infinitely many x intercepts? (Select all that apply)

<p>Tangent (A), Sine (B)</p> Signup and view all the answers

Name the families that have end behaviors of $x \to \pm \infty$ with $y \to \pm \infty$ in opposite directions.

<p>Cubic, cube root</p> Signup and view all the answers

Which families have exactly one x intercept? (Select all that apply)

<p>Cubic (A), Cube Root (B), Log (C)</p> Signup and view all the answers

Which function families only have end behavior on one end? (Select all that apply)

<p>Square Root (A), Log (B)</p> Signup and view all the answers

Which functions are periodic? (Select all that apply)

<p>Tangent (A), Sine (B)</p> Signup and view all the answers

Which families have vertical line symmetry? (Select all that apply)

<p>Sine (A), Quadratic (B)</p> Signup and view all the answers

Which families have rotational point symmetry? (Select all that apply)

<p>Sine (A), Tangent (B), Cubic (C), Cube Root (E)</p> Signup and view all the answers

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Study Notes

Function Families and Their Properties

  • Linear and Quadratic Functions: Have all real numbers for the domain.
  • Cubic, Cube Root, Logarithmic, and Tangent Functions: Have all real numbers for the range.
  • Exponential, Quadratic, and Rational Functions: May have no x-intercepts.
  • Linear, Logarithmic, Square Root, Rational, and Tangent Functions: May have no y-intercepts.
  • Tangent, Logarithmic, and Rational Functions: Have vertical asymptotes, where the function approaches infinity as it approaches a specific x-value.
  • Exponential and Rational Functions: Have horizontal asymptotes, where the function approaches a specific y-value as x approaches infinity or negative infinity.
  • Linear, Quadratic, Cubic, Rational, Cube Root, and Exponential Functions: Define end behavior for both ends as x approaches positive or negative infinity.
  • Sine and Tangent Functions: Feature infinitely many x-intercepts, repeating their values periodically.
  • Cubic and Cube Root Functions: Exhibit end behaviors where one side approaches positive infinity while the other approaches negative infinity.
  • Cubic, Cube Root, and Logarithmic Functions: Each has exactly one x-intercept, where the function crosses the x-axis.
  • Logarithmic and Square Root Functions: Display end behavior on only one end, either approaching infinity as x approaches negative or positive infinity.
  • Sine and Tangent Functions: Recognized as periodic functions, repeating their output at regular intervals.
  • Quadratic and Sine Functions: Have vertical line symmetry, meaning they are mirrored across a vertical axis.
  • Tangent, Cube Root, Sine, Cubic, and Rational Functions: Feature rotational point symmetry, where the graph maintains its shape when rotated around a central point.

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