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?
Signup and view all the answers
The range of the function is represented as R: [0, ∞)
Signup and view all the answers
What does the Quadratic Parent Function represent?
Signup and view all the answers
How do you move a function up?
Signup and view all the answers
What is the Cubic Parent Function?
Signup and view all the answers
What is the definition of a vertical shrink?
Signup and view all the answers
What does the Absolute Value Parent Function represent?
Signup and view all the answers
How do you reflect a function over the y-axis?
Signup and view all the answers
What is the equation for the Exponential Parent Function?
Signup and view all the answers
How do you move a function down?
Signup and view all the answers
What is the definition of inverse functions?
Signup and view all the answers
What is meant by the domain of a function?
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
