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Questions and Answers
What is a parent function?
What is a parent function?
The most basic function in a family of functions.
What is the linear parent function?
What is the linear parent function?
y = x or f(x) = x. The simplest form of a linear equation.
What is the quadratic parent function?
What is the quadratic parent function?
y = x^2 or f(x) = x^2.
What is the exponential parent function?
What is the exponential parent function?
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What does it mean to transform parent functions?
What does it mean to transform parent functions?
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What are translations of parent functions?
What are translations of parent functions?
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What is reflection of parent functions?
What is reflection of parent functions?
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What does rotation of parent functions involve?
What does rotation of parent functions involve?
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What is slope-intercept form?
What is slope-intercept form?
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What is function notation?
What is function notation?
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What is the domain of a function?
What is the domain of a function?
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What is the range of a function?
What is the range of a function?
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What are integer operations?
What are integer operations?
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What is the distributive property?
What is the distributive property?
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Study Notes
Parent Functions
- Most basic function within a family of functions that serves as a reference point for transformations.
Linear Parent Function
- Represented by the equation y = x or f(x) = x.
- Known as the simplest form of a linear equation.
Quadratic Parent Function
- Defined by the equation y = x² or f(x) = x².
- Characteristic U-shaped graph.
Exponential Parent Function
- Expressed in the form y = ab^x.
- Models exponential growth or decay.
Transformations of Parent Functions
- Modifications of parent functions create different members within the same family of graphs.
Translations of Parent Functions
- Involves adding constants k or h to shift the graph horizontally (left/right) or vertically (up/down).
Reflection of Parent Functions
- Involves multiplying x or y values to reflect the graph over the y-axis or x-axis.
Rotation of Parent Functions
- Involves rearranging x and y values, potentially multiplying by a negative factor, to rotate graphs by angles of 90, 180, 270, and 360 degrees, in both clockwise and counter-clockwise directions.
Slope-Intercept Form
- Written as y = mx + b, where m is the slope and b is the y-intercept.
Function Notation
- Represented as f(x) = ?, indicating the output value of a function f for a specific input x.
Domain
- Refers to the set of all possible x values for which a function is defined.
Range
- Refers to the set of all possible y values that a function can output.
Integer Operations
- Focus on operations involving signed numbers, detailing rules for adding, subtracting, multiplying, and dividing positive and negative integers.
Distributive Property
- Defined by the equation a(b + c) = ab + ac, illustrating how multiplication distributes over addition.
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Description
Explore the essential concepts of parent functions and their transformations with these flashcards. Each card defines key terms and equations relevant to various types of functions, including linear, quadratic, and exponential. Perfect for visual learners and students preparing for exams.
