3.4 Graphing Techniques; Transformations

1
3.4 Graphing Techniques Transformations
2
(No Transcript)
3
(2, 6)
(1, 3)
(2, 4)
(1, 1)
(0, 2)
(0, 0)
4
(No Transcript)
5
(2, 4)
(0, 0)
(1, 1)
(2, 1)
(1, -2)
(0, -3)
6
Vertical Shifts

• cgt0 The graph of f(x)c
  is the same as the graph of f(x) but shifted UP
  by c.
• For example c 2 then f(x)2 shifts f(x) up by
  2.

• clt0 The graph of f(x)c
  is the same as the graph of f(x) but shifted DOWN
  by c.
• For example c -3 then f(x)(-3) f(x)-3
  shifts f(x) down by 3.

7
(No Transcript)
8
(No Transcript)
9
Horizontal Shifts
If the argument x of a function f is replaced by
x-h, h a real number, the graph of the new
function y f(x-h) is the graph of f shifted
horizontally left (if h lt 0) or right (if h gt 0).
10
(No Transcript)
11
(No Transcript)
12
Reflections about the x-Axis and the y-Axis

• The graph of g - f(x) is the same as graph of
  f(x) but reflected about the x-axis.
• The graph of g f(-x) is the same as graph of
  f(x) but reflected about the y-axis.

13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
Compression and Stretches

• The graph of yaf(x) is obtained from the graph
  of yf(x) by vertically stretching the graph if a
  gt 1 or vertically compressing the graph if 0 lt a
  lt 1.
• The graph of yf(ax) is obtained from the graph
  of yf(x) by horizontally compressing the graph
  if a gt 1 or horizontally stretching the graph if
  0 lt a lt 1.

20
(No Transcript)