Podcast
Questions and Answers
Which function families always have all real numbers for the domain? (Select all that apply)
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)
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)
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)
Which function families may have no y intercepts? (Select all that apply)
Which functions have vertical asymptotes? (Select all that apply)
Which functions have vertical asymptotes? (Select all that apply)
Which functions have horizontal asymptotes? (Select all that apply)
Which functions have horizontal asymptotes? (Select all that apply)
Which functions have defined end behavior for both ends as $x \to \infty$?
Which functions have defined end behavior for both ends as $x \to \infty$?
Which function family has infinitely many x intercepts? (Select all that apply)
Which function family has infinitely many x intercepts? (Select all that apply)
Name the families that have end behaviors of $x \to \pm \infty$ with $y \to \pm \infty$ in opposite directions.
Name the families that have end behaviors of $x \to \pm \infty$ with $y \to \pm \infty$ in opposite directions.
Which families have exactly one x intercept? (Select all that apply)
Which families have exactly one x intercept? (Select all that apply)
Which function families only have end behavior on one end? (Select all that apply)
Which function families only have end behavior on one end? (Select all that apply)
Which functions are periodic? (Select all that apply)
Which functions are periodic? (Select all that apply)
Which families have vertical line symmetry? (Select all that apply)
Which families have vertical line symmetry? (Select all that apply)
Which families have rotational point symmetry? (Select all that apply)
Which families have rotational point symmetry? (Select all that apply)
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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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