1. 1.5b Combining Transformations

2. Let’s start with a problem:
Describe a basic graph and a sequence of transformations
that can be used to produce a graph of the given function. 2
Starting with y = x ,
Does the order with
which we apply these
transformations matter???
translate right 3 units,
vertically stretch by 2,
and translate down 4 units.

3. Combining Transformations
Apply the following transformations, in order, to the graph of
the squaring function. Graph the result.
a horizontal shift 2 units to the right
a vertical stretch by a factor of 3
a vertical translation 5 units up
Expand the final result!!!

4. Combining Transformations
Apply the following transformations, in order, to the graph of
the squaring function. Graph the result.
a horizontal shift 2 units to the right
a vertical stretch by a factor of 3
a vertical translation 5 units up
Now, apply the same transformations, but in the opposite order.
Expand the final result!!!
The Moral: Order often matters when stretches, shrinks, or
reflections are involved…

5. More Practice Starting with y = x , horizontally shrink by 1/3
Describe a basic graph and a sequence of transformations
that can be used to produce a graph of the given function. 3
Starting with y = x ,
horizontally shrink by 1/3
and translate up 2 units.

6. More Practice
The graph of y = f(x) is shown. Determine the graph of the
given composite function by showing the effect of a sequence
of transformations on the graph of y = f(x).

7. More Practice A vertical stretch by a factor of 2
The graph of y = f(x) is shown. Determine the graph of the
given composite function by showing the effect of a sequence
of transformations on the graph of y = f(x).
A vertical stretch
by a factor of 2

8. More Practice A horizontal translation 1 unit to the left
The graph of y = f(x) is shown. Determine the graph of the
given composite function by showing the effect of a sequence
of transformations on the graph of y = f(x).
A horizontal
translation 1
unit to the left

9. More Practice A vertical translation 3 units down
The graph of y = f(x) is shown. Determine the graph of the
given composite function by showing the effect of a sequence
of transformations on the graph of y = f(x).
A vertical
translation 3
units down

10. White board… Describe the translations to vertical shrink of ¼
horizontal shrink of 1/3, shift down 4
shift 2 left, reflection across y- axis, horizontal shrink of ¼, vertical shrink of ½, shift 3 up
Homework: p , 31, Quiz tomorrow sections !