Transformation-of-graphs.docx - Transformation of graphs...

Transformation of graphs
Remember: inside the brackets affects the x-coordinate, but the opposite way.
outside the brackets affects the y-coordinate.
Describing transformations examples
Graph 1: y = f(x)
Graph 2: the graph has moved 2 to the
right, so we have added 2 to the
x-coordinate.
inside the brackets affects the
x-coordinate, but the opposite way
so graph 2  f(x – 2)
Graph 1: y = f(x)
Graph 2: the y-coordinates are now all
negative – they have been
multiplied by -1.
outside the brackets affects the
y-coordinate.
so graph 2  -1f(x)
Graph 1: y = f(x)
Graph 2: the graph has moved 1 down,
so we have subtracted 1 from the
y-coordinate.
outside the brackets affects the
y-coordinate
so graph 2  f(x) - 1
Graph 1: y = f(x)
Graph 2: the y-coordinates have been
multiplied by 3.
outside the brackets affects the
y-coordinate
so graph 2  3f(x)
1
2 1
2
2
1
1
2

1
1
1
1
Affect x
or y?
(-12, 5)
becomes
(18, -8)
becomes
f(x + 3) x (-15, 5) (15, -8)
f(x – 4)
f(x) + 2
f(x) – 3
f(3x)
f(½x)
2f(x)
½ f(x)
f(-x)
-f(x)