Transformations of graphs
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Flip to reveal answersWhat does y = f(x) + b do to the graph?
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All 8 Flashcards — Transformations of graphs
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Question
What does y = f(x) + b do to the graph?
Answer
Translates it UP by b (b outside f changes the height; negative b moves it down).
Question
What does y = f(x − a) do, and why the sign?
Answer
Translates RIGHT by a. The input must be a units larger to reproduce an old height, so features move to bigger x.
Question
What does y = p·f(x) do?
Answer
Vertical stretch by factor p (every height ×p). Points on the x-axis don't move.
Question
What does y = f(qx) do?
Answer
Horizontal stretch by factor 1/q (width scaled by the reciprocal). q > 1 squashes toward the y-axis.
Question
What does y = −f(x) do?
Answer
Reflects the graph in the x-axis (heights flip sign).
Question
What does y = f(−x) do?
Answer
Reflects the graph in the y-axis (left↔right).
Question
Under g(x) = p f(x − a) + b, where does a point (x, y) go?
Answer
To (x + a, p·y + b): inside shifts x, outside scales then shifts y.
Question
If f has horizontal asymptote y = 0, what is the asymptote of f(x) + 5?
Answer
y = 5 — the outside +5 lifts the whole graph, asymptote included.
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Full study notes for Transformations of graphs
Topic 2.8 hub
Graph transformations (HL only)
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