Function Transformations
A free Algebra II lesson from the “Transformations of Functions” unit, with a worked example and practice problems including step-by-step solutions.
Transformations change a parent function. Adding outside shifts up or down, changing inside parentheses shifts left or right, and multiplying by a negative reflects a graph.
What you'll learn
- Identify shifts and reflections
- Use transformation notation
- Connect algebraic changes to graph changes
Worked example
Problem. Describe y = (x - 3)^2 + 4 compared with y = x^2.
- x - 3 inside the square shifts the graph right 3.
- +4 outside shifts the graph up 4.
- The shape is still a parabola.
Answer: right 3 and up 4
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. y = f(x) + 6 shifts the graph...
Choices: Up 6 · Down 6 · Right 6 · Left 6
Show solution
- Adding outside changes outputs.
Answer: Up 6
2. y = f(x - 4) shifts the graph...
Choices: Right 4 · Left 4 · Up 4 · Down 4
Show solution
- Inside changes feel backward.
Answer: Right 4
3. y = -f(x) reflects the graph across the...
Choices: x-axis · y-axis · line y = x · origin only
Show solution
- The outputs change sign.
Answer: x-axis
4. The vertex of y = (x + 2)^2 - 5 is...
Choices: (-2, -5) · (2, -5) · (-2, 5) · (2, 5)
Show solution
- Vertex form gives (h, k).
Answer: (-2, -5)
5. y = 3f(x) creates a...
Choices: Vertical stretch by 3 · Horizontal shift right 3 · Reflection · Vertical shift up 3
Show solution
- Multiplying outside scales outputs.
Answer: Vertical stretch by 3
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