© Daniel Holloway
Transforming graphs is not too dissimilar
from transforming shapes. Whereas you
can translate, rotate, reflect and enlarge
shapes; you can translate, stretch and
reflect graphs.
We use the notation f(x) to denote a
function of x. A function of x is any
algebraic expression where x is the only
variable.
There are six rules you need to learn about
transforming graphs. To show these rules,
we will use the following graph. This is the
graph y = f(x)
Rule 1: This is a translation of the graph in
the vector (a0 ) in the y-direction
y = f(x) + a
Rule 2: This is a translation of the graph in
the vector ( a0 ) in the x-direction
y = f(x – a)
Rule 3: This is a stretch of the graph by a
scale factor of k in the y-direction
y = kf(x)
Note that
they cross
at the x
axis
Rule 4: This is a stretch of the graph by a
scale factor of 1/t in the x-direction
Note that
they cross
at the y
axis
y = f(tx)
Rule 5: This is a reflection of the graph in the
x-axis
y = -f(x)
Rule 6: This is a reflection of the graph in the
y-axis
y = f(-x)
y
y
5
-5
0
The grid shows the graph of
y=x2 for -2 ≤ x ≤ 2
5
5 x
-5
0
5 x
The dotted line shows the same
graph. Describe the transformation
taking it to the new line on the grid.
y = (x + 3) 2
y
y
5
-5
0
The grid shows the graph of
y=x2 for -2 ≤ x ≤ 2
5
5 x
-5
0
5 x
The dotted line shows the same
graph. Describe the transformation
taking it to the new line on the grid.
y = x2 - 2
y
y
5
-5
0
The grid shows the graph of
y=x2 for -2 ≤ x ≤ 2
5
5 x
-5
0
5 x
The dotted line shows the same
graph. Describe the transformation
taking it to the new line on the grid.
y = 2x2