Maths Unit 3 Difficult Topics

Transformations of Functions - Key Points

Y (always outside brackets) the transformations are parallel to the y axis

• y = f(x) +a --> Moves the graph up a units (if negative it moves the graph down a units)
• y = af(x) --> Stretched (or squashed if x/a) vertically [y axis]
• y = -f(x) --> Reflection in the x axis

X (always inside brackets) the transformations are parallel to the x axis

• y = f(x+a) --> Moves graph to the left if + and to the right if -
• y = f(ax) --> Squashed (or stretched if x/a) horizontally [x axis]
• y + f(-x) --> Reflection in the y axis

Others

• y = af (x/a) --> enlargement, scale factor a, centre is origin of y = f(x)
• y = -f(-x) --> rotation by 180degrees aboout the origin of y = f(x)

Congruence and Similarity

• Congruence means exactly the same…