Thinkwell Algebra 2 Chapter 1.2 Flashcards

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.