Transformations
Practice Flashcards
What does y = f(x) + k do?
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All Flashcards in Topic 2.11
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2.11.18 cards
What does y = f(x) + k do?
Translates the graph up by k (down if k < 0) — an outside change, as expected.
What does y = f(x − a) do?
Translates the graph RIGHT by a — inside changes move the opposite way.
Why does f(x − 3) move right, not left?
To get the same output, x must be 3 bigger, so the graph sits 3 to the right.
y = f(x + 2) moves the graph which way?
Left 2 (inside +2 is the opposite of its sign).
Translation vector for f(x − a) + b?
Top a (right), bottom b (up).
Image of (3, 5) under y = f(x − 2) + 1?
(5, 6) — right 2, up 1.
Do asymptotes and intercepts translate too?
Yes — every feature slides by the same vector.
Which changes act on x, which on y?
Inside f acts on x (left/right, opposite sign); outside f acts on y (up/down, as written).
2.11.29 cards
What does y = a·f(x) do?
Stretches the graph vertically by factor a (every y ×a).
What does y = f(bx) do?
Stretches the graph horizontally by factor 1/b (the reciprocal).
f(2x) — stretch or squash, and by how much?
Squash horizontally by factor 1/2 (the graph narrows).
What does y = −f(x) do?
Reflects the graph in the x-axis (y-coordinates flip sign).
What does y = f(−x) do?
Reflects the graph in the y-axis (x-coordinates flip sign).
Image of (2, 5) under y = 3f(x)?
(2, 15) — multiply y by 3.
Image of (2, 5) under y = f(−x)?
(−2, 5) — negate x.
Which transformations does a vertical stretch leave fixed?
The x-intercepts (their y is 0, so 0 × a = 0).
Outside vs inside changes — what do they affect?
Outside the function affects y; inside affects x (reciprocal for stretch, opposite for shift/flip).
2.11.39 cards
What does y = a·f(x) + k combine?
A vertical stretch by a, then a translation k up — both on the y-values.
For 2f(x) − 1, in what order do you transform y?
Multiply by 2 first (stretch), then subtract 1 (translate).
Why isn't 2f(x) − 1 the same as 2(f(x) − 1)?
Stretch before translate: ×2 then −1, not −1 then ×2.
Image of (1, 4) under y = 3f(x)?
(1, 12) — multiply y by 3, x unchanged.
Image of (2, 3) under y = f(x − 1) + 5?
(3, 8) — right 1, up 5.
How do you describe y = f(x − 2) + 5?
A translation 2 right and 5 up (vector (2, 5)).
How do you describe y = −f(x) + 4?
A reflection in the x-axis, then a translation 4 up.
In a·f(b(x − h)) + k, which parts are horizontal?
The inside ones: stretch by 1/b, then translate right h.
What words do exams want for 'describe the transformation'?
Translation / stretch (scale factor) / reflection (in which axis), with direction and amount.
Topic 2.11 study notes
Full notes & explanations for Transformations
Math AA SL exam skills
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