Questions and Answers
What is the Linear Parent Function?
f(x) = x
What is the Absolute Value Parent Function?
f(x) = |x|
What is the Quadratic Parent Function?
f(x) = x^2
What is the Absolute Value Equation?
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What is Reflection in graph transformations?
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What is Vertical Translation?
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What is Vertical Stretch?
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What is Vertical Shrink?
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What is the Constant Equation?
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What does +/- a number inside the function do?
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What does +/- a number outside the function do?
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What is Horizontal Translation?
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Study Notes
Parent Functions
- Linear Parent Function: A foundational function characterized by a constant rate of change, represented graphically as a straight line.
- Absolute Value Parent Function: Produces a V-shaped graph, reflecting the magnitude of a number without regard to its sign.
- Quadratic Parent Function: Forms a parabolic curve, demonstrating the relationship between variables squared.
Parent Function Equations
- Linear Parent Equation: Defined as f(x) = x, its graph is a straight line through the origin with a slope of 1.
- Absolute Value Equation: Expressed as f(x) = |x|, with a vertex at the origin and a U-shaped graph.
- Quadratic Equation: Expressed as f(x) = x², producing a parabola that opens upward.
- Constant Equation: Defined as f(x) = 1, producing a horizontal line at y = 1.
Transformations
- Reflection: Changes the orientation of the graph by flipping it across the x-axis or y-axis.
- Vertical Translation: Adjusts the graph's position vertically, moving it up or down along the y-axis.
- Horizontal Translation: Alters the position of the graph horizontally, moving it left or right along the x-axis.
- Vertical Stretch: Occurs when a function is multiplied by a factor greater than one, resulting in a steeper graph.
- Vertical Shrink: Happens when a multiplying factor lies between 0 and 1, making the graph flatter.
Function Shifts
- +/- a number inside the function: Affects the graph's horizontal position, shifting it left or right based on the value added or subtracted.
- +/- a number outside the function: Influences the graph's vertical position, shifting it up or down depending on whether the value is positive or negative.
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Description
This quiz focuses on key parent functions and their transformations, ideal for Algebra 2 students. You'll explore definitions and equations for linear, absolute value, and quadratic parent functions. Test your knowledge and enhance your understanding of this foundational concept in algebra.
