Transformations and symmetry

Sections

1. 5A Translations of known graphs Shift a graph left, right, up and down by changing its equation, and use translations to find the vertex of a parabola or the centre of a circle.
2. 5B Reflections in the axes Reflect a graph in the y-axis by replacing x with −x, in the x-axis by replacing y with −y, and in both axes at once (a rotation of 180° about the origin).
3. 5C Even and odd functions Recognise even functions (symmetric in the y-axis) and odd functions (symmetric about the origin), and test any function algebraically by substituting −x.
4. 5D Horizontal and vertical dilations Stretch a graph horizontally by replacing x with x/a, vertically by multiplying the function by b, and handle fractional and negative factors.
5. 5E The absolute value function Absolute value as distance from zero, its piecewise definition, graphs of y = a|x − h| + k, solving absolute value equations, and useful identities.
6. 5F Composite functions Form composite functions f(g(x)) and g(f(x)), evaluate them, and find the domain and range of a composite.
7. 5G Combining transformations Apply several transformations in order, write the resulting equation, and know which pairs of transformations commute and which do not.
8. 5H Continuity and piecewise-defined functions What it means for a function to be continuous at a point, how to sketch piecewise-defined functions, and how to test whether the pieces join up.