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Pre Calculus 11 Notes
By:
Gen L.
Lesson 2: Graphing Using Transformations
Terms
Scalar: a value which scales the function's outputs.
: the transposed value of
, compared to the parent graph.
: the transposed value of
, compared to the parent graph.
Simple Cases
The simpleist function is
and is the parent graph.
All other parabolas are transpositions of the parent.
Table of Values
x
y
-2
4
0
0
2
4
Simple Cases
Another easy one is
. All
values are inverted.
Table of Values
x
y
-2
-4
0
0
2
-4
Transposition w/o
scalar
Look at the function
. This function is similar to the parent, but the vertex is different.
In this case, the vertex is
.
Table of Values
x
y
x'
y'
-2
4
0
1
0
0
2
-3
2
4
4
1
Transposition w/
scalar
Look at the function
. This is similar to the previous, but the function is scaled by
.
All values are multiplied by
when graphed.
Table of Values
x
y
x'
y'
-2
4
-1
-2
0
0
1
6
2
4
3
-2
Transposition w/ fractional scalar
Look at the function
. Again, similar to previous, but scaled by
.
Table of Values
x
y
x'
y'
-2
4
-5
-3
0
0
-3
-5
2
4
-1
-3
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