SECT. 1.2TRANSLATIONS AND FUNCTIONS
© Copyright All Rights Reserved Homework Depot www.BCMath.ca
I) TRANSLATIONS:
Translations: (Graphically) sliding an object withoutrotating/changing its shape
There are two types of translations
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
Vertical Translation (Up/Down)
Horizontal Translation (Left/Right)
© Copyright All Rights Reserved Homework Depot www.BCMath.ca
II) HORIZONTAL TRANSLATIONS (HT)
A H.T. occurs when the x-variable is changed byadding/subtracting a constant
Draw a circle around the “x”only, ignore any exponentssquares, radicals, ….
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-1
1
2
3
4
5
6
7
8
Graph is shifted
3 units to the right
© Copyright All Rights Reserved Homework Depot www.BCMath.ca
x
y
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
-1
1
2
3
4
5
6
7
8
EX: GIVEN THE FOLLOWING EQUATIONSA) GRAPH BOTH EQUATIONS,B) INDICATE WHAT TRANSLATIONS OCCURRED
x
y
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
-1
1
2
3
4
5
6
7
8
Graph is shifted
4 units to the LEFT
© Copyright All Rights Reserved Homework Depot www.BCMath.ca
III) VERTICAL TRANSLATIONS (VT)
A VT occurs when the y-variable is changed to any-variable adding/subtracting a constant
Draw a circle around the “y”only, ignore any exponentssquares, radicals, ….
Graph is shifted
3 units Down
Isolate the Y-variable!!!
© Copyright All Rights Reserved Homework Depot www.BCMath.ca
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-1
1
2
3
4
5
6
7
8
EX: GIVEN THE FOLLOWING EQUATIONSA) GRAPH BOTH EQUATIONS,B) INDICATE WHAT TRANSLATIONS OCCURRED
Graph is shifted 2 units UP
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-1
1
2
3
4
5
6
7
8
© Copyright All Rights Reserved Homework Depot www.BCMath.ca
IV) SUMMARY
i) Horizontal Translation: Change with the X-variable
Horizontal Shift of 3 Units RIGHT!
Horizontal Shift of 3 Units LEFT!
Vertical Shift of 3 Units UP!
Vertical Shift of 3 Units DOWN!
ii) Vertical Translation: Change with the Y-variable
© Copyright All Rights Reserved Homework Depot www.BCMath.ca
PRACTICE: INDICATE THE TRANSLATION FOR EACH OF THEFOLLOWING EQUATIONS
HS: 3 Units
Left
HS: 4 Units Right!!
VS: 5 Units
Down!!
HS: 1 Unit Left !!
VS: 3 Units UP!!
© Copyright All Rights Reserved Homework Depot www.BCMath.ca
EX: INDICATE WHICH OF THE FOLLOWING IS THE CORRECTTRANSLATION
a)9 units down c) 9 units up
b)9 units left d) 9 units right
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
© Copyright All Rights Reserved Homework Depot www.BCMath.ca
EX: GIVEN THAT THE COORDINATES (A,B) IS ON THEGRAPH OF , INDICATE WHAT COORDINATESWILL BE ON THE GRAPH OF
3 units to the right
2 units up
© Copyright All Rights Reserved Homework Depot www.BCMath.ca