Objectives:
1. To perform SRT
transformations on
the graphs of
functions
•
•
•
•
•
•
Assignment:
P. 71-2: 45, 46, 50, 5359 odd
P. 79-80: 6, 7, 10, 12
P. 81: 23, 24, 41, 44,
49
P. 83: 74
SRT Worksheet
Read: P. 56, 58-60
Scaling
Translating
Reflecting
One of the handiest ways to graph a function is
by transformations on parent functions. This
includes scaling, reflecting, and translating;
what we’ll call SRT.
Each of these transformations (scaling,
reflecting, and translating) come in a vertical,
y, and a horizontal, x, variety.
y  a  f (c   x  h)  k
You will be able to vertically
scale the graph of
a function.
If you are given the graph
of the function y = f (x),
then the graph of
y  a  f ( x)
is scaled vertically by a
factor of a.
• Stretch if a > 1
• Shrink if 0 < a < 1
y  x2
y
1 2
x
4
If you are given the graph
of the function y = f (x),
then the graph of
y  a  f ( x)
is scaled vertically by a
factor of a.
• The y-coordinate is what
is multiplied by a
y  x2
y
1 2
x
4
By hand, graph each of the following on the
same coordinate plane:
1. y  x 2
2. y  3x
2
1 2
3. y  x
3
You will be able to reflect the graph of a
function across the x-axis
If you are given the graph
of the function y = f (x),
then the graph of
y  a  f ( x)
• If a < 0, then the graph is
reflected across the xaxis
y  x2
y   x2
By hand, graph each of the following on the
same coordinate plane:
1. y  x3
2. y   x
3
You will be able to
horizontally scale
the graph of a function
If you are given the graph
of the function y = f (x),
then the graph of
y  f (c  x )
is scaled horizontally by a
factor of c.
• Shrink if c > 1
• Stretch if 0 < c < 1
y  sin  x 
y  sin  2 x 
If you are given the graph
of the function y = f (x),
then the graph of
y  f (c  x )
is scaled horizontally by a
factor of c.
• The x-coordinate is
multiplied by 1/c.
y  sin  x 
y  sin  2 x 
It might also seem a bit weird that a and c work
in opposite or inverse directions. Again, this is
not all that weird if you consider that a is
really on the wrong side of the equation:
y  a  f (c  x )
1
y  f (c  x )
a
It might also seem a bit weird that a and c work
in opposite or inverse directions. Again, this is
not all that weird if you consider that a is
really on the wrong side of the equation:
y  3 5 x
1
y  5 x
3
This is still a vertical stretch by a factor of 3.
Notice that f (1/2)
equals g(1). It’s
just that this
point occurs later
on g than on f.
It has been
stretched
horizontally.
f  x  x
2
1 
g  x   x 
2 
2
By hand, graph each of the following on the
same coordinate plane:
1. y  x 2
2. y   2 x 
2
1 
3. y   x 
2 
2
You will be able to reflect
the graph of a function
across the y-axis
If you are given the graph
of the function y = f (x),
then the graph of
y  f (c  x )
• If c < 0, then the graph is
reflected across the yaxis
y  x3
y   x3
By hand, graph each of the following on the
same coordinate plane:
1. y  x
2. y   x
You will be able to perform SRT
transformations on the graph of a function
Let’s say that for whatever reason, some mad
mathematician came up with an equation that had
multiple transformations. If you were to graph the
thing, do so in this order:
y  a  f (c   x  h)  k
1. Scaling: Multiply y-values by a and x-values by 1/c
2. Reflecting: If a is negative, flip over x-axis; if c is
negative flip over y-axis
3. Translating: Move left/right for h*, up/down for k
When performing a horizontal stretch/shrink
together with a horizontal shift, you have to
put the function into the form:
y  f (c   x  h)
This means that you will have to factor out the
c-value.
2
  1 
 3x  1   3  x   
  3 
2
By hand, graph each of the following on the
same coordinate plane:
1. y  x 2
2
1

2. y  2  x  1  4
3

The graph of y = f (x)
is shown. Use SRT
transformations to
sketch the graph of
the each function.
1. y = 2  f (x)
2. y = −f (2x + 6) – 1
•
Objectives:
1. To perform SRT
transformations on
the graphs of
functions
•
•
•
•
•
Assignment:
P. 71-2: 45, 46, 50, 5359 odd
P. 79-80: 6, 7, 10, 12
P. 81: 23, 24, 41, 44,
49
P. 83: 74
SRT Worksheet