VERTICAL AND HORIZONTALTRANSFORMATION OF A FUNCTION.

Last Friday, We learned about the vertical and horizontal translations of a given function.

REVIEW: VERTICAL TRANSLATION

y=f(x)+k

y=f(x)-k

Where K is responsible for the vertical movement of the whole function.

EXAMPLE :

A. f(x)=x²

B. f(x)+2

SOLUTION:From parent function.The whole graph will move 2 points up.

You can also use table of values.

X	Y
-2 -1 0 1 2	( -2)2 + 2 4+2 =6 ( -1)2 + 2 1+2 =3 ( 0)2 + 2 0+2 =2 (1)2 + 2 1+2 =3 (2)2 + 2 4+2 =6

C. f(x)-4

SOLUTION:From parent function.The whole graph will move 4 points down.

You can also use table of values.

X	Y
-2 -1 0 1 2	( -2)2 -4 4-4 =0 ( -1)2 -4 1-4 =-3 ( 0)2 -4 0-4 =-4 (1)2 -4 1-4 =-3 (2)2 +-4 4-4 =0

NOTE: Given the equation of y=f(x)+ k , The x value does not change(x, y+ k ).

REVIEW: HORIZONTAL TRANSLATION

y=f(x-h)

y=f(x+h)

Where H is responsible for the horizontal movement of the whole function.

ALWAYS remember to read the H value as OPPOSITE.

EXAMPLE :

A. f(x)=x²

B. f(x-4)

SOLUTION:From parent function.The whole graph will move 4 points to the right.

You can also use table of values.

X	Y
3 4 5	( 3-4)2 -1^2 =1 ( 4-4)2 02 =0 ( 5-4)2 12 =1

C. f(x+3)

SOLUTION:From parent function.The whole graph will move 3 points to the left.

X	Y
-4 -3 -2	( -4+3)2 -12 =1 ( -3=3)2 02 =0 ( -2+3)2 12 =1

NOTE: Given the equation of y=f(x+ h) , The y value does not change(x+ h,y)

QUICK EXAMPLE

:COMBINATION OF VERTICAL AND HORIZONTAL TRANSLATION

graph y=(x+3)² +4

SOLUTION:

Starting from parent function y=x² , The whole graph will move 3 points to the left because of (x+3)²[remember we read h as opposite].From (x+3)² , the graph will move four points down because of the k value +4 from the equation (x+3)² + 4.