Questions and Answers
What is a relation?
What is the domain in a relation?
The set of all of the possible x-values (inputs).
What does the range refer to in a relation?
The set of all the possible y-values (outputs).
What defines a function?
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The Vertical Line Test (VLT) determines if a relation is a function.
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What is the independent variable in a function?
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What is a dependent variable?
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What does the function notation f(x) represent?
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What is a transformation in geometry?
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Name the four types of transformations.
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What is an image in relation to transformations?
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What is the preimage of a transformation?
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What is reflection in geometric transformations?
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What does translation describe in transformations?
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What is a rotation in geometry?
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What is dilation in geometric transformations?
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What do compression functions do?
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What is the effect of stretch functions on a graph?
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What occurs during vertical compression?
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What happens during a vertical stretch?
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What does horizontal compression do to a graph?
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What is the effect of a horizontal stretch on a graph?
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What is a parent function?
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What is the constant parent function?
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What is the linear parent function?
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What is the quadratic parent function?
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What is the cubic parent function?
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What is the square root parent function?
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What is rotation in terms of transformations?
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What is reflection in transformations?
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What does translation refer to in transformations?
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Study Notes
Relations and Functions
- A relation is defined as a set of ordered pairs (x,y), representing inputs and outputs.
- The domain consists of all possible x-values (inputs) in a relation.
- The range includes all possible y-values (outputs) from a relation.
- A function is a specific type of relation where each input corresponds to exactly one output.
Identifying Functions
- The Vertical Line Test (VLT) determines if a relation is a function; if a vertical line intersects the graph at more than one point, the relation is not a function.
Variables in Functions
- The independent variable (x) is the input that influences the output.
- The dependent variable (y) is the output that depends on the input.
Function Notation
- Function Notation (f(x)) represents the output of a function in terms of its input. It can be used to simplify expressions by substituting values into x.
Transformations
- A transformation alters a figure's position, size, or shape.
- Four primary types of transformations include:
- Reflection: A mirrored image across a specific line.
- Translation: A slide of the figure in a particular direction.
- Rotation: Circular movement around a fixed point, keeping equal distance from the center.
- Dilation: Adjusts the size while maintaining the shape.
Compression and Stretching
- Compression functions narrow the graph, pulling it towards the axis.
- Stretch functions widen the graph, pushing it away from the axis.
Vertical Transformations
- Vertical Compression: Shrinks the graph towards the x-axis by reducing y-values (multiplying by a factor less than 1).
- Vertical Stretch: Expands the graph upwards by increasing y-values (multiplying by a factor greater than 1).
Horizontal Transformations
- Horizontal Compression: Squeezes the graph toward the y-axis, reducing x-values (multiplying x by a factor greater than 1).
- Horizontal Stretch: Expands the graph sideways, increasing x-values (multiplying x by a fraction).
Parent Functions
- The parent function is the simplest form of a function before any transformations.
- Constant Parent Function: f(x) = c
- Linear Parent Function: f(x) = x
- Quadratic Parent Function: f(x) = x²
- Cubic Parent Function: f(x) = x³
- Square Root Parent Function: f(x) = √x
Additional Definitions
- An image refers to the resulting shape after a transformation.
- The preimage is the original figure before any transformation is applied.
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Description
Test your knowledge of key concepts in Algebra 2 with these flashcards from Chapter 1.2. This includes important terms like relation, domain, range, and function. Each term is defined to enhance your understanding of functions and their properties.