Unit 3 Parent Functions and Transformations Homework 3 Answer Key provides a comprehensive guide to understanding the fundamental principles of parent functions and their transformations. This resource delves into the core concepts, empowering students to master the intricacies of mathematical transformations and their impact on graphical representations.
By exploring the characteristics and properties of parent functions, learners gain a solid foundation for understanding how transformations alter the shape, position, and orientation of graphs. This knowledge is essential for navigating higher-level mathematics and real-world applications.
Unit 3 Parent Functions
Parent functions are basic functions that serve as building blocks for more complex functions. They have distinct characteristics and properties that determine the shape and behavior of their graphs.
Common parent functions include:
- Linear function: f(x) = mx + b
- Quadratic function: f(x) = ax^2 + bx + c
- Cubic function: f(x) = ax^3 + bx^2 + cx + d
- Exponential function: f(x) = a^x
- Logarithmic function: f(x) = log a(x)
Each parent function has its own unique graph and set of properties that distinguish it from other functions.
Transformations of Parent Functions
Transformations are operations that can be applied to parent functions to create new functions with different graphs. Common transformations include:
- Translations: Moving the graph horizontally or vertically
- Reflections: Flipping the graph across the x-axis or y-axis
- Stretches: Making the graph taller or wider
- Compressions: Making the graph narrower or shorter
Transformations can significantly alter the shape and behavior of a parent function, making it essential to understand how they affect the graph.
Homework 3 Answer Key
| Question | Answer |
|---|---|
1. Graph the function f(x) = x^2
|
 = x^2
- 4.png) |
| 2. Find the equation of the function that is the translation of f(x) = x^3 + 2 units to the right. | f(x) = (x
|
3. Sketch the graph of the function g(x) =
|
 =
-2|x| + 1.png) |
Practice Problems, Unit 3 parent functions and transformations homework 3 answer key
- Graph the function h(x) = log2(x
1) + 3.
- Find the equation of the function that is the reflection of f(x) = x^2 + 4 across the x-axis.
- Sketch the graph of the function k(x) = 2(x
- 3)^2
- 1.
Answer Key for Practice Problems:
- h(x) = log 2(x – 1) + 3:
 = log_2(x
- 1) + 3.png)
- Reflection of f(x) = x^2 + 4 across the x-axis: f(x) =-(x^2 + 4) = -x^2 – 4
- k(x) = 2(x – 3)^2 – 1:
 = 2(x
- 3)^2
- 1.png)
Additional Resources
- Khan Academy: Parent Functions
- Math is Fun: Transformations of Functions
- Purple Math: Transformations of Functions
Question Bank: Unit 3 Parent Functions And Transformations Homework 3 Answer Key
What are the different types of parent functions?
Common parent functions include linear, quadratic, cubic, exponential, and logarithmic functions.
How do transformations affect the graph of a parent function?
Transformations can translate, reflect, stretch, or compress the graph of a parent function, altering its shape, position, or orientation.
What is the purpose of Homework 3 Answer Key?
Homework 3 Answer Key provides step-by-step solutions to assigned homework problems, aiding students in checking their work and reinforcing their understanding.
