📚 Topic Summary
Function transformations change the appearance of a graph. Vertical stretches and compressions affect the y-values of a function, making the graph taller or shorter. Horizontal stretches and compressions affect the x-values, widening or narrowing the graph. Remember, vertical transformations are often more intuitive, while horizontal transformations can seem "backwards". Mastering these concepts unlocks a deeper understanding of functions and their behavior.
🧠 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Vertical Stretch |
A. Transformation that multiplies all x-values by a factor. |
| 2. Vertical Compression |
B. Transformation that divides all y-values by a factor between 0 and 1. |
| 3. Horizontal Stretch |
C. Transformation that divides all x-values by a factor between 0 and 1. |
| 4. Horizontal Compression |
D. Transformation that multiplies all y-values by a factor greater than 1. |
| 5. Transformation |
E. A change made to the function rule that will affect its graph. |
✍️ Part B: Fill in the Blanks
A ___________ stretch occurs when we multiply the ___________-values of a function by a factor greater than 1. A horizontal ___________ happens when we multiply the x-values by a factor between 0 and 1. Understanding the difference between vertical and horizontal transformations can be ___________, but with practice, it becomes easier. Remember that horizontal transformations affect the ___________-axis.
🤔 Part C: Critical Thinking
Explain, in your own words, how the graph of $y = 2f(x)$ differs from the graph of $y = f(2x)$. Be specific about the type of transformation involved and how it affects the graph's shape and size.