📚 Topic Summary
Transformations in Algebra 2 involve altering the graph of a function. Multiple transformations combine several operations, such as shifts, stretches, compressions, and reflections. Understanding the order in which these transformations are applied is crucial for accurately graphing the transformed function. The general form can be represented as $y = a \cdot f(b(x - h)) + k$, where $a$ affects vertical stretch/compression/reflection, $b$ affects horizontal stretch/compression/reflection, $h$ represents horizontal shifts, and $k$ represents vertical shifts.
To perform multiple transformations, apply them in the correct order: horizontal shifts, horizontal stretches/compressions/reflections, vertical stretches/compressions/reflections, and finally vertical shifts. Remember to work from the inside out, following the order of operations.
🧠 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Vertical Stretch |
A. A transformation that flips the graph over the x-axis. |
| 2. Horizontal Compression |
B. A transformation that shifts the graph left or right. |
| 3. Reflection over x-axis |
C. A transformation that makes the graph narrower horizontally. |
| 4. Vertical Shift |
D. A transformation that makes the graph taller. |
| 5. Horizontal Shift |
E. A transformation that shifts the graph up or down. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words: vertical, horizontal, reflection, stretch, compression.
When transforming a function, a number multiplied outside the function causes a _________ _________ or _________. A number multiplied inside the function results in a _________ _________ or _________. A negative sign outside the function creates a _________ over the x-axis. Changes to $x$ affect the graph _________ while changes to $y$ affect the graph _________.
🤔 Part C: Critical Thinking
Explain, in your own words, the importance of applying transformations in the correct order. Provide an example to illustrate your point.