SECTION 2 2 HORIZONTAL AND VERTICAL TRANSLATIONS I

I) TRANSLATIONS: Translations: (Graphically) sliding an object without rotating/changing its shape There are two

II) HORIZONTAL TRANSLATIONS (HT) A H. T. occurs when the x-variable is changed by

EX: GIVEN THE FOLLOWING EQUATIONS A) GRAPH BOTH EQUATIONS, B) INDICATE WHAT TRANSLATIONS OCCURRED

III) VERTICAL TRANSLATIONS (VT) A VT occurs when the y-variable is changed to an

IV) SUMMARY i) Horizontal Translation: Change with the X-variable Horizontal Shift of 3 Units

PRACTICE: INDICATE THE TRANSLATION FOR EACH OF THE FOLLOWING EQUATIONS HS: 3 Units Left

EX: INDICATE WHICH OF THE FOLLOWING IS THE CORRECT TRANSLATION a) 9 units down

EX: GIVEN THAT THE COORDINATES (A, B) IS ON THE GRAPH OF , INDICATE

Challenge: What are the values of “a” , “b”, and “c” if the function

Slides: 12

Download presentation

SECTION 2. 2 HORIZONTAL AND VERTICAL TRANSLATIONS

I) TRANSLATIONS: Translations: (Graphically) sliding an object without rotating/changing its shape There are two types of translations Vertical Translation (Up/Down) y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 © Copyright All Rights Reserved Homework Depot www. BCMath. ca Horizontal Translation (Left/Right) y 5 4 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 x

II) HORIZONTAL TRANSLATIONS (HT) A H. T. occurs when the x-variable is changed by adding/subtracting a constant Draw a circle around the “x” only, ignore any exponents squares, radicals, …. y 8 7 6 5 Graph is shifted 3 units to the right 4 3 2 1 -5 -4 -3 -2 -1 0 1 -1 x 2 3 4 5 © Copyright All Rights Reserved Homework Depot www. BCMath. ca

EX: GIVEN THE FOLLOWING EQUATIONS A) GRAPH BOTH EQUATIONS, B) INDICATE WHAT TRANSLATIONS OCCURRED y 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 x -7 -6 -5 -4 -3 -2 -1 0 1 2 3 -1 Graph is shifted 4 units to the LEFT © Copyright All Rights Reserved Homework Depot www. BCMath. ca x

III) VERTICAL TRANSLATIONS (VT) A VT occurs when the y-variable is changed to an y-variable adding/subtracting a constant Draw a circle around the “y” only, ignore any exponents squares, radicals, …. y Isolate the Y-variable!!! 8 7 6 5 4 3 2 1 -5 -4 -3 -2 -1 0 -1 x 1 2 3 4 5 -2 -3 -4 © Copyright All Rights Reserved Homework Depot www. BCMath. ca Graph is shifted 3 units Down

EX: GIVEN THE FOLLOWING EQUATIONS A) GRAPH BOTH EQUATIONS, B) INDICATE WHAT TRANSLATIONS OCCURRED y 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 Graph is shifted 2 units UP © Copyright All Rights Reserved Homework Depot www. BCMath. ca x

IV) SUMMARY i) Horizontal Translation: Change with the X-variable Horizontal Shift of 3 Units RIGHT! Horizontal Shift of 3 Units LEFT! ii) Vertical Translation: Change with the Y-variable Vertical Shift of 3 Units UP! Vertical Shift of 3 Units DOWN! © Copyright All Rights Reserved Homework Depot www. BCMath. ca

PRACTICE: INDICATE THE TRANSLATION FOR EACH OF THE FOLLOWING 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 CORRECT TRANSLATION a) 9 units down b) 9 units left y 5 4 4 3 3 2 2 1 x c) 9 units up d) 9 units right 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -2 -3 -3 -4 -4 -5 -5 © Copyright All Rights Reserved Homework Depot www. BCMath. ca x

EX: GIVEN THAT THE COORDINATES (A, B) IS ON THE GRAPH OF , INDICATE WHAT COORDINATES WILL BE ON THE GRAPH OF 3 units to the right 2 units up © Copyright All Rights Reserved Homework Depot www. BCMath. ca

Challenge: What are the values of “a” , “b”, and “c” if the function in the left is shifted 4 units right and 2 units down to result with the function on the right?

Amc 12 a 2008