Questions and Answers
What is a horizontal shrink?
The domain of the function is represented as D: [0, ∞)
Non-negative real numbers
What does the Linear Parent Function represent?
f(x) = x
How do you reflect a function over the x-axis?
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The range of the function is represented as R: [0, ∞)
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What does the Quadratic Parent Function represent?
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How do you move a function up?
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What is the Cubic Parent Function?
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What is the definition of a vertical shrink?
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What does the Absolute Value Parent Function represent?
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How do you reflect a function over the y-axis?
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What is the equation for the Exponential Parent Function?
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How do you move a function down?
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What is the definition of inverse functions?
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What is meant by the domain of a function?
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Study Notes
Transformations in Algebra 2
- Horizontal Shrink: Occurs when x-values are multiplied by a number greater than 1 inside the function f(ax).
- Vertical Shrink: Achieved by multiplying the function by a fraction (less than 1) on the outside, affecting y-values as af(x).
- Vertical Stretch: Involves multiplying the function by a number greater than 1 on the outside, which also affects y-values as af(x).
- Horizontal Stretch: Happens when x-values are multiplied by a fraction (less than 1) inside the function f(ax).
Parent Function Domain & Range
- Domain & Range [0, ∞): Functions that have a domain starting from 0 and extending to infinity, reflecting graph characteristics like the Square Root or Absolute Value functions.
- Domain & Range (-∞, ∞): Functions with unrestricted x-values and y-values, such as the Linear, Cubic, and Cube Root parent functions.
- Absolute Value Function: Has a range of [0, ∞) with the equation f(x) = |x|.
Movement of Functions
- Movement Up: Achieved by adding a constant outside the function (f(x) + k).
- Movement Down: Involves subtracting a constant outside the function (f(x) - k).
- Move Left: Addition inside the function (f(x + k)) shifts the graph to the left.
- Move Right: Subtracting a constant within the function (f(x - k)) shifts the graph to the right.
Parent Functions
- Linear Parent Function: Represented by f(x) = x; domain is (-∞, ∞) and range is (-∞, ∞).
- Quadratic Parent Function: Typically represented by f(x) = x²; domain is (-∞, ∞) and range is [0, ∞).
- Cubic Parent Function: Defined by f(x) = x³; domain and range are both (-∞, ∞).
- Cube Root Parent Function: Denoted by f(x) = ∛x; domain and range are (-∞, ∞).
- Square Root Parent Function: Given by f(x) = √x; domain is [0, ∞) and range is also [0, ∞).
- Absolute Value Parent Function: Expressed as f(x) = |x|; domain is (-∞, ∞) and range is [0, ∞).
- Exponential Parent Function: Defined as f(x) = a^x, generally with domain (-∞, ∞) and range (0, ∞).
Reflections
- Reflects Over x-axis: Achieved by multiplying the function by -1 outside (-f(x)).
- Reflect Over y-axis: Implemented by multiplying the x-values by -1 inside the function (f(-x)).
Inverse Functions
- Defined by the condition that if f(g(x)) = g(f(x)) = x, then f(x) and g(x) are considered inverses of each other.
General Concept of Domain
- Domain refers to all possible x-values that a function can accept.
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Description
Test your knowledge of transformations and parent functions in Algebra 2 with this comprehensive review. This quiz covers key concepts such as horizontal shrink, domain and range, and more, providing a thorough understanding of unit transformations.