A parent function generates a family of functions that are related to the parent by a combination of _____?
Information provided by a parent on an enrollment form can be shared with unauthorized persons only if _______ gives written consent.A. an agent from the state licensing agencyB. the parentC. a staff memberD. the program director
Transformations
transformations :)
A parent function generates a family of functions that are related to the parent by a combination of transformations. To understand this, let's break it down step by step:
1. Start with the parent function: A parent function is a basic function, typically represented by a simple equation, that serves as a starting point for creating related functions. Examples of parent functions include linear functions (y = mx + b), quadratic functions (y = ax^2 + bx + c), and exponential functions (y = ab^x).
2. Apply transformations: To create different functions within the family, we apply various transformations to the parent function. These transformations involve changes such as shifting, stretching/compressing, reflecting, and vertical/horizontal scaling.
- Shifting: Shifting a function involves moving it left/right (horizontal shift) or up/down (vertical shift). This is done by adding or subtracting values inside the function equation.
- Stretching/Compressing: Stretching or compressing a function alters its slope or curvature. It is achieved by multiplying or dividing either the x or y-coordinate values by a constant.
- Reflecting: Reflecting a function involves flipping it across an axis. It can be a vertical reflection (flipping it vertically) or a horizontal reflection (flipping it horizontally). This is usually achieved by adding a negative sign to either the x or y-coordinate values.
3. Combination of transformations: To create different members of the function family, we can apply a combination of these transformations. For example, you can shift a function to the right and then stretch it vertically, or you can reflect it horizontally and then shift it up. These combinations lead to a variety of functions that share similarities with the parent but have distinct characteristics due to the applied transformations.
In summary, a parent function generates a family of functions through the use of transformations, such as shifting, stretching, reflecting, and scaling. These transformations allow us to create a range of related functions that share the same underlying structure but exhibit different graphical properties.