Function Transformations and Compositions
Master the key concepts of translating, reflecting, stretching, compressing, and composing functions.
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Questions Covered in This Set
10 cards to master
What transformation does f(x) + k represent?
A vertical shift up by k units (or down if k is negative)
What transformation does f(x - h) represent?
A horizontal shift right by h units (or left if h is negative)
How does -f(x) transform the graph of f(x)?
It reflects the graph across the x-axis (flips vertically)
How does f(-x) transform the graph of f(x)?
It reflects the graph across the y-axis (flips horizontally)
What does a·f(x) do when |a| > 1?
Creates a vertical stretch, making the graph taller
What does f(b·x) do when |b| > 1?
Creates a horizontal compression, making the graph narrower
What is the correct order for applying multiple transformations?
1) Horizontal shift/stretch, 2) Reflections, 3) Vertical stretch, 4) Vertical shift
What does (f ∘ g)(x) mean?
f(g(x)) - the composition of f and g, where g(x) is substituted into f
Is f ∘ g the same as g ∘ f?
No, order matters in function composition. Generally f(g(x)) ≠ g(f(x))
What determines the domain of f(g(x))?
Values in the domain of g where g(x) is also in the domain of f
