http://www.ck12.org Chapter 1. Functions and Graphs
This transformation shifts the entire graph down 5 units.
3)g(x)→−g( 2 x)
This transformation is a vertical reflection across thexaxis and a horizontal compression by a factor of 2.
4)j(x) =j(−x 2 )
This transformation is a horizontal reflection across theyaxis and a horizontal stretch by a factor of 2. A common
misconception is to see the^12 and believe that thexvalues will be half as big which is a horizontal compression. How-
ever, thexvalues need to be twice as big to counteract this factor of^12.
Vocabulary
Horizontalcomes from the word horizon and means flat.
Verticalmeans up and down.
Shiftis a rigid transformation that means the shape keeps the exact shape.
Stretchis a scaled transformation.
Guided Practice
- Describe the following transformation in words:g(x)→ 2 g(−x)
- Describe the transformation that would changeh(x)in the following ways:
- Vertical compression by a factor of 3.
- Vertical shift down 4 units.
- Horizontal shift right 5 units.
- Describe the transformation that would changef(x)in the following ways:
- Horizontal stretch by a factor of 4 and a horizontal shift 3 units to the right.
- Vertical reflection across thexaxis and a shift down 2 units.
Answers:
- Vertical stretch by a factor of 2 and a reflection across theyaxis.
2.^13 h(x− 5 )− 4
3.−f(^14 (x− 3 ))−2 or−f(^14 x−^34 )− 2
Practice
Describe the following transformations in words.
1.g(x)→−g(−x)
2.f(x)→−f(x+ 3 )
3.h(x)→h(x+ 1 )− 2
4.j(x)→j(−x+ 3 )
5.k(x)→−k( 2 x)
6.f(x)→ 4 f(^12 x+ 1 )