Transcript 1.1 Transformations

Bell Ringer
Plot each point on
graph paper.You will
attach graph paper
to Bell Ringer sheet.
1. A(0,0)
2. B(5,0)
3. C(–5,0)
D
C
Domain ?
Range ?
A
Intercepts
4. D(0,5)
5. E(0, –5)
E

B
Holt McDougal Common Core Edition
1.1  1.4
F-IF.6
A-REI.1
F-BF.3
Correlation
Slope
Reflection
Regression
Stretch
Transformation vs. Translation
Parent Function
Slope tree
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Example: Translating Points
Perform the given translation on the point (–3, 4).
Give the coordinates of the translated point.
5 units right
Translating (–3, 4) 5 units
right results in the point
(2, 4).

(-3, 4)

(2, 4)
? Slope ?
? Domain ?
? Range ?
Example: Translating Points
Perform the given translation on the point (–3, 4).
Give the coordinates of the translated point.
2 units (–3, 4)
2 units left and 3 units down
Translating (–3, 4) 2 units
left and 3 units down results
in the point (–5, 1).

3 units

(–5, 1)
Example: Translation
Perform the given translation on the point (–1, 3). Give
the coordinates of the translated point.
4 units right
Translating (–1, 3) 4 units
right results in the point
(3, 3).


(–1, 3)
(3, 3)
? Slope ?
Example: Translation
Perform the given translation on the point (–1, 3). Give
the coordinates of the translated point.
1 unit left and 2 units down
1 unit
Translating (–1, 3) 1 unit
left and 2 units down results
in the point (–2, 1).

(–1, 3)
2 units
? Slope ?

(–2, 1)
Notice that when you translate
left or right, the x-coordinate changes,
and when you translate
up or down, the y-coordinate changes.
Translations
Horizontal Translation
Vertical Translation
Bell Ringer
Using complete sentence, correlate the
“h” and “k” to “x” and “y”.
Translations
Horizontal Translation
Vertical Translation
vocabulary
ACT
You can transform a function by
transforming its ordered pairs. When a
function is translated or reflected, the
original graph and the graph of the
transformation are congruent because the
size and shape of the graphs are the same.
Start 4 page packet
You need to be responsible and keep up with it
We will work on each day
It is not homework yet
You graphed y=x on a graphing calculator by pressing
y= and entering y1=x.
Then pressed graph.
Then you entered and graphed y2 = x + 5.
Next you entered and graphed y3= x – 5.
Exit Question: How does the term congruent explain
how a change in the value of k in the equation
y=x + k affects the equation’s graph.
On graph paper. You may use the same piece from
yesterday’s Bell Ringer.
Perform the given translation on the point (-3, 4).
Indicate the coordinates of the translated point.
This is two different translations.
a) 5 units right
b) 2 unit left and 2 units down
Reflections
Reflection Across y-axis
Reflection Across x-axis
Example
translation 2 units up
Identify important points from the graph and make a table.
X
-5
-2
0
2
5
Y
-3
0
-2
0
-3
Y+ 2
-3 + 2 = -1
0+2=2
-2 + 2 = 0
0+2=2
-3 + 2 = -1
? (green)Slope(s) ?
Add 2 to each y-coordinate.
The entire graph shifts 2 units up.
Team of no more than 2; winning
group gets prize!
Example
Use a table to perform the transformation of y = f(x). Use
the same coordinate plane as the original function.
steps
translation 3 units right
x
y
x+3
–2
4
–2 + 3 = 1
–1
0
–1 + 3 = 2
0
2
0+3=3
Add 3 to each x-coordinate.
What did you do?
The entire
graph
shifts 3 units right.
What
happened?
1) What axis are you changing
2) Id key points on original graph
3) Plot new ordered pairs
Example
Steps
??
Use a table to perform the transformation of y = f(x).
Use the same coordinate plane as the original function.
reflection across x-axis
x
y
–y
–2
4
–4
–1
0
0
0
2
–2
2
2
–2
Multiply each y-coordinate by –1.
The entire graph flips across the x-axis.
f
Example Business Application
The graph shows the cost of
painting based on the number of
cans of paint used. Sketch a graph
to represent the cost of a can of
paint doubling, and identify the
transformation of the original graph
that it represents.
Read
only
If the cost of painting is based on
the number of cans of paint used
and the cost of a can of paint
doubles, the cost of painting also
doubles. This represents a vertical
stretch by a factor of 2.
Perform each transformation of y = f(x). Use the same coordinate plane as the original
function. Copy the original function. Create a table. You can do all on graph paper
a) Translate 2 units
up
b) Reflection across x axis