1.3. Point Notation and Function Notation http://www.ck12.org
f(x)→−^12 f(x− 1 )+ 3
Answers:
1.f(x)→− 2 f(x− 1 )+ 4
Vertical reflection across thexaxis. Vertical stretch by a factor of 2. Vertical shift 4 units. Horizontal shift right one
unit.
(x,y)→(x+ 1 ,− 2 y+ 4 )
2.(x,y)→( 3 x+ 1 ,−y+ 7 )
Horizontal stretch by a factor of 3 and then a horizontal shift right one unit.
Vertical reflection over thexaxis and then a vertical shift 7 units up.
f(x)→−f(^13 x−^13 )+ 7
3.f(x)→−^12 f(x− 1 )+ 3
Vertical reflection across thexaxis, stretch by a factor of^12 and shift up 3. Horizontal shift right 1 unit.
(x,y)→(x+ 1 ,−^12 y+ 3 )
Practice
Convert the following function notation into words and then point notation. Finally, apply the transformation to
three example points.
TABLE1.4:
x y
0 5
1 6
2 71.f(x)→−^12 f(x+ 1 )
2.g(x)→ 2 g( 3 x)+ 2
3.h(x)→−h(x− 4 )− 3
4.j(x)→ 3 j( 2 x− 4 )+ 1
5.k(x)→−k(x− 3 )
Convert the following functions in point notation to function notation.