Graph Transformations

Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.

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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)

f(x + a) shifts LEFT by a (the sign looks backwards). f(x) + a shifts UP by a. The shape never changes.

For y to match the old value at x = 0 we need x + 3 = 0, so x = −3. The curve has slid 3 left.

−f(x) turns peaks into troughs. f(−x) mirrors the curve left to right.

y = 2sin(x) doubles the amplitude. y = sin(2x) squashes the wave to half its width.

translation	a slide that moves a graph without changing its shape or size
reflection	a flip that mirrors the graph in the x-axis or y-axis
stretch	scaling a graph taller/shorter or wider/narrower
scale factor	the number every coordinate is multiplied by in a stretch
amplitude	the maximum height of a wave from its centre line
period	the horizontal length of one full cycle of a wave
image	the new position of a point after a transformation
vertex	the turning point of a parabola (its lowest or highest point)

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