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Flip to reveal answersWhat does y = a·f(x) + k combine?
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All 9 Flashcards — Combined transformations
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Question
What does y = a·f(x) + k combine?
Answer
A vertical stretch by a, then a translation k up — both on the y-values.
Question
For 2f(x) − 1, in what order do you transform y?
Answer
Multiply by 2 first (stretch), then subtract 1 (translate).
Question
Why isn't 2f(x) − 1 the same as 2(f(x) − 1)?
Answer
Stretch before translate: ×2 then −1, not −1 then ×2.
Question
Image of (1, 4) under y = 3f(x)?
Answer
(1, 12) — multiply y by 3, x unchanged.
Question
Image of (2, 3) under y = f(x − 1) + 5?
Answer
(3, 8) — right 1, up 5.
Question
How do you describe y = f(x − 2) + 5?
Answer
A translation 2 right and 5 up (vector (2, 5)).
Question
How do you describe y = −f(x) + 4?
Answer
A reflection in the x-axis, then a translation 4 up.
Question
In a·f(b(x − h)) + k, which parts are horizontal?
Answer
The inside ones: stretch by 1/b, then translate right h.
Question
What words do exams want for 'describe the transformation'?
Answer
Translation / stretch (scale factor) / reflection (in which axis), with direction and amount.
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Full study notes for Combined transformations
Topic 2.11 hub
Transformations
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