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Questions and Answers
Which of the following best defines a parent function in mathematics?
Which of the following best defines a parent function in mathematics?
Which of the following is the parent function of the family of quadratic equations?
Which of the following is the parent function of the family of quadratic equations?
Which of the following describes how the graph of y = x^2 - 4x + 7 is related to the graph of the parent function y = x^2?
Which of the following describes how the graph of y = x^2 - 4x + 7 is related to the graph of the parent function y = x^2?
Which of the following functions is likely to have a parent function of y = \sin(x)?
Which of the following functions is likely to have a parent function of y = \sin(x)?
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Which of the following statements is true about parent functions?
Which of the following statements is true about parent functions?
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Study Notes
Definition of Parent Function
- A parent function is the simplest form of a function type, serving as a prototype for a family of functions.
- It is used as a reference to understand transformations like shifts, stretches, and reflections.
Parent Function of Quadratic Equations
- The parent function of the quadratic family is ( y = x^2 ).
- This function generates the basic shape of a parabola centered at the origin.
Relationship Between Quadratic Functions
- The graph of ( y = x^2 - 4x + 7 ) is a transformed version of the parent function ( y = x^2 ).
- This specific quadratic may involve vertical shifts and horizontal translations compared to the parent function.
Functions with Sine Parent Function
- A likely candidate for having a parent function of ( y = \sin(x) ) includes periodic sinusoidal functions, such as ( y = \sin(x + 2) ) or ( y = 3\sin(x) ).
- These functions maintain the wave-like behavior characteristic of sine functions while allowing for transformations.
True Statements About Parent Functions
- Parent functions provide a foundation for understanding more complex variations within their respective families.
- They illustrate key properties and behaviors that are retained in the transformations of related functions.
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Description
Test your knowledge of parent functions in mathematics with this quiz. Learn about the core representation of function types and identify the parent function in various families, such as quadratic equations.
