Questions and Answers
What is the linear function parent?
What is the linear graphing form?
y-y1=m(x-x1)
What is the quadratic parent function?
What is the quadratic graphing form?
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What is the absolute value function parent?
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What is the absolute value graphing form?
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What is the square root function parent?
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What is the square root graphing form?
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What is the cubic function parent?
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What is the cubic function graphing form?
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What is the cube root function parent?
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What is the cube root graphing form?
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What is the exponential function parent?
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What is the reciprocal parent function?
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What is a function?
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What does 'a' tell you in an equation?
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What does 'h' tell you in an equation?
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What does 'k' tell you in an equation?
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What are transformations in graphing?
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What is absolute value?
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What does 'range' mean in mathematics?
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What does 'domain' mean in mathematics?
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Study Notes
Parent Functions Overview
- Linear Function Parent: Defined by the equation f(x) = x, representing a straight line through the origin.
- Quadratic Function Parent: Characterized by f(x) = x², resulting in a parabolic curve that opens upwards.
- Absolute Value Function Parent: Expressed as f(x) = |x|, displaying a "V" shape graph, indicating distance from zero.
- Square Root Function Parent: Given by f(x) = √x, featuring a graph that starts at the origin and increases gradually.
- Cubic Function Parent: Defined by f(x) = x³, producing an S-shaped curve crossing through the origin.
- Cube Root Function Parent: Given by f(x) = ∛x, which produces a curve allowing all real numbers.
- Exponential Function Parent: Represented by f(x) = 2^x, revealing rapid growth for positive x values.
- Reciprocal Function Parent: Defined by f(x) = 1/x, featuring two hyperbolas in opposite quadrants.
Graphing Forms
- Linear Graphing Form: y - y₁ = m(x - x₁), representing a line on a graph using a point and a slope.
- Quadratic Graphing Form: y = a(x - h)² + k, providing transformations through vertex form with 'a', 'h', and 'k'.
- Absolute Value Graphing Form: y = a|x - h| + k, indicating transformations of the absolute value function.
- Square Root Graphing Form: y = a√(x - h) + k, involving vertical/horizontal stretches and shifts of the square root function.
- Cubic Graphing Form: y = a(x - h)³ + k, translating cubic functions while adjusting its steepness.
- Cube Root Graphing Form: y = a∛(x - h) + k, similar transformations applicable as in other parent functions.
Function Characteristics
- Function Definition: A relation connecting inputs to unique outputs, ensuring each input corresponds to only one output.
- One-to-One Function: Each input maps to a unique output, and vice versa, ensuring no value is repeated in either domain or range.
- Domain: Represents all possible x values that can be plugged into a function without resulting in undefined outputs.
- Range: Encompasses all potential y values produced by the function as outputs across the domain.
Transformations and Features
- Transformations: Graph alterations such as stretching, compressing, or reflecting, that retain the type of graph.
- Absolute Value: Defines the numerical distance of any value from zero on the number line.
- Parameter 'a': Indicates vertical stretch/shrink of the graph and shows reflection across the x-axis if negative.
- Parameter 'h': Represents horizontal shifts, determining how far right (positive) or left (negative) the graph moves.
- Parameter 'k': Determines vertical shifts, indicating movement up (positive) or down (negative) from the original graph position.
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Test your knowledge of algebra parent functions with these flashcards. Each card presents a key concept, including definitions and graphing forms of linear, quadratic, and absolute value functions. Perfect for students looking to reinforce their understanding of these essential algebraic concepts.