MathIsimple

Function Transformations

Master function transformations! Learn how to shift, stretch, shrink, and reflect functions to create new graphs.

9th Grade
Functions
~60 min
🎮 Interactive Activity: Transformation Explorer

Explore how transformations affect functions!

Original:

f(x) = x²
↓

Transformed:

f(x) = (x - 2)² + 3
🎮 Interactive Activity: Scaling Explorer

See how scaling affects functions!

Original:

f(x) = x²
↓

Scaled:

f(x) = 2x²
1. Vertical Shifts

Vertical Translations

Adding or subtracting a constant shifts the graph up or down.

f(x) + k

k > 0: Shifts graph up k units

k < 0: Shifts graph down |k| units

Example: f(x) = x² + 3 shifts x² up 3 units

Example: f(x) = x² - 2

Transformation: Shift x² down 2 units

Effect: Every point moves 2 units down

2. Horizontal Shifts
3. Vertical & Horizontal Scaling
4. Reflections
Frequently Asked Questions

Practice Time!

Practice Quiz
10
Questions
0
Correct
0%
Score
1
What transformation does f(x) + 3 represent?
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2
What transformation does f(x - 2) represent?
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3
What does -f(x) do to the graph?
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4
What does f(-x) do to the graph?
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5
What transformation does 2f(x) represent?
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6
What does f(2x) do to the graph?
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7
How does f(x) - 4 transform the graph?
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8
What is the effect of f(x + 3)?
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9
What does 0.5f(x) do to the graph?
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10
Which transformation combines f(x - 2) + 3?
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