Here’s a vocabulary list with definitions, descriptions, and examples for the terms you've provided:
Horizontal Stretch
- Definition: A horizontal stretch occurs when a function is transformed by a factor that expands its width along the x-axis. This is typically represented by replacing x with a fraction of x (e.g., f(kx) where 0 < k < 1).
- Example: For the function f(x) = x², applying a horizontal stretch by a factor of 2 gives f(1/2x) = (1/2x)² = (1/4)x², which stretches the parabola.
Parent Function
- Definition: The simplest form of a function of a particular type, which serves as a model for other functions.
- Example: The parent function for linear functions is f(x) = x, and for quadratic functions, it is f(x) = x².
Reflection
- Definition: A reflection is a transformation that flips a function over a specified line, such as the x-axis or y-axis.
- Example: Reflecting the function f(x) = x² over the x-axis results in f(x) = -x².
Slope
- Definition: The slope of a line is a measure of its steepness, typically represented as the ratio of the rise over the run between two points on the line.
- Example: For the line passing through the points (2, 3) and (4, 7), the slope is (7-3)/(4-2) = 4/2 = 2.
Transformation
- Definition: A transformation refers to changing the position, size, or shape of a graph through various operations such as shifts, stretches, compressions, and reflections.
- Example: The graph of f(x) = x² can be transformed to g(x) = (x - 3)² + 2 by shifting right 3 units and up 2 units.
Translation
- Definition: A translation is a transformation that shifts a graph horizontally, vertically, or both without altering its shape or size.
- Example: Translating f(x) = x² up by 2 units results in g(x) = x² + 2.
Vertical Compression
- Definition: A vertical compression occurs when a function is multiplied by a factor between 0 and 1, reducing its height.
- Example: For the function f(x) = x² and applying a vertical compression by a factor of 1/2 gives g(x) = 1/2 * x².
Vertical Reflection
- Definition: A vertical reflection is a transformation that flips a graph over the x-axis.
- Example: Reflecting f(x) = x³ over the x-axis results in f(x) = -x³.
Vertical Shift
- Definition: A vertical shift moves a graph up or down on the coordinate plane.
- Example: Shifting the graph of f(x) = x² up by 3 units results in g(x) = x² + 3.
Vertical Stretch
- Definition: A vertical stretch occurs when a function is multiplied by a factor greater than 1, increasing its height.
- Example: For f(x) = x², applying a vertical stretch by a factor of 3 results in g(x) = 3*x².
Lesson 6 Vocabulary
Even Function
- Definition: An even function is one for which f(-x) = f(x) for all x in its domain, indicating symmetry about the y-axis.
- Example: The function f(x) = x² is even because f(-x) = (-x)² = x².
Odd Function
- Definition: An odd function is one for which f(-x) = -f(x) for all x in its domain, indicating symmetry about the origin.
- Example: The function f(x) = x³ is odd because f(-x) = (-x)³ = -x³.
Feel free to ask for further clarification or additional examples for any of the terms!