CAIE: A Level - Mathematics 9709 - Pure Mathematics 1

Functions / Transformation of Functions

KEYPOINTS:

TRANSLATION

f(x + a) is a horizontal translation of –a

Move the graph to the left if (a > 0) or right if (a < 0)

f(x) + a is a vertical translation of a

Move the graph up if (a > 0) or down if (a < 0)

REFLECTION

–f(x) is a reflection in the x–axis
f(–x) is a reflection in the y–axis

STRETCH / COMPRESS

af(x) is a stretch with factor a in the y–direction

If a > 1 OR a < –1, graph is stretched vertically

If –1 < a < 1, graph is compressed vertically

f(ax) is a stretch with factor \(\frac{1}{a}\) in the x–direction

If a > 1 OR a < –1, graph is compressed horizontally

If –1 < a < 1, graph is stretched horizontally

Past Papers Topic Wise Questions A Level: Mathematics 9709 - Pure Mathematics 1 Functions | Transformation of Functions

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