Transformations of Functions
A free College Algebra lesson from the “Transformations of Functions” unit, with a worked example and practice problems including step-by-step solutions.
Function transformations change a graph predictably. Outside changes affect outputs, inside changes affect inputs, and negative factors create reflections.
What you'll learn
- Identify shifts
- Identify reflections and stretches
- Apply transformation notation
Worked example
Problem. Describe y = f(x - 3) + 4.
- x - 3 inside shifts the graph right 3.
- +4 outside shifts up 4.
- The graph keeps the same basic shape.
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: Down 6 · Up 6 · Right 6 · Left 6
Show solution
- Outside subtraction shifts down.
Answer: Down 6
2. y = f(x + 2) shifts the graph...
Choices: Left 2 · Right 2 · Up 2 · Down 2
Show solution
- Inside changes feel backward.
Answer: Left 2
3. y = -f(x) reflects across the...
Choices: x-axis · y-axis · line y = x · origin only
Show solution
- Outputs change sign.
Answer: x-axis
4. g(x) = f(x) + 5 shifts f...
Choices: Up 5 · Down 5 · Left 5 · Right 5
Show solution
- Adding outside moves the graph vertically.
Answer: Up 5
5. g(x) = f(x - 3) shifts f...
Choices: Right 3 · Left 3 · Up 3 · Down 3
Show solution
- Inside -3 shifts right.
Answer: Right 3
Practice this interactively with instant feedback and an AI tutor.
Practice Transformations of Functions Take the free placement check