Transformations and Shifts
Practice predicting how equation changes move, stretch, or flip a graph.
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Questions Covered in This Set
12 cards to master
f(x) + k does what to the graph?
Shifts it UP k units (outside changes act as expected).
f(x − h) does what to the graph?
Shifts it RIGHT h units — inside changes act opposite the sign.
f(x + h) does what to the graph?
Shifts it LEFT h units.
What is the inside/outside rule?
Outside the function affects y-values and behaves as expected; inside affects x-values and behaves backwards.
What does a·f(x) do when a > 1?
Vertical stretch by factor a — graph gets taller/narrower. If 0 < a < 1 it flattens.
What does −f(x) do?
Reflects the graph over the x-axis (negates y-values only).
What does f(−x) do?
Reflects the graph over the y-axis (left–right mirror).
Vertex of y = a(x − h)² + k?
(h, k) — vertex form is just the shifted parent parabola.
Shift f(x) = x² right 4 and down 1. Write g(x).
g(x) = (x − 4)² − 1, vertex at (4, −1).
If f(3) = 7 and g(x) = f(x − 2) + 4, find g(5).
g(5) = f(3) + 4 = 11 — it's really a substitution problem.
How do you read f(2x − 6) correctly?
Factor first: f(2(x − 3)) = horizontal compression by 1/2 AND shift right 3.
Parabola with x-intercepts 1 and 5 shifted 3 left — new intercepts?
−2 and 2; horizontal shifts move x-intercepts by the same amount.
