### Online College Courses for Credit

#### FREE EDUCATIONAL RESOURCES PROVIDED by SOPHIA

##### Are you a student?
Free Professional Development
+

# Horizontal and Vertical Translation

##### Rating:
(2)
• (2)
• (0)
• (0)
• (0)
• (0)
Author: Kitty Black
##### Description:

Y= a [ b ( x - h ) ] + k

Be able to use and understand 'k' and 'h'

The equation for transformation is :

Y= a [ b ( x -/+ h ) ] +/- k

Each variable has its own job in that equation. For starters we will learn about h and k.

h is used for horizontal transition either left or right.

k is used for vertical transition either up or down.

(more)

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*

No credit card required

29 Sophia partners guarantee credit transfer.

312 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 27 of Sophia’s online courses. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.

Tutorial
• A translation can move the graph of a function up or down ( Vertical Translation ) and right or left ( Horizontal Translation ).
• A vertical translation of function y=f(x) by k units is written in either y-k=f(x) or y=f(x)+k.
• ​If k>0, then the graph moves up.
• ​y=f(x)+4, the graph ends up moving 4 units up.
• If k<0, then the graph moves down.
• ​y=f(x)-3, the graph ends up moving 3 units down.
• A horizontal translation of function y=f(x) by h units is written y=f(x-h).
• ​If h>0, then the graph moves right.
• ​y=f(x-6), the graph ends up moving 6 units to the right.
• If h<0, then the graph moves left.
• ​y=f(x+3), the graph ends up moving 3 units to the left.
• Vertical and Horizontal translations can be combines to form y=f(x-h)+k
• ​y=f(x-3)+2
• ​This causes the graph to move 3 units to the right, and 2 units up.