October 07, 2009
October 07, 2009
1.6 Graphical Transformations
functions that map real numbers to real numbers
Rigid transformations: size and shape are unchanged
(translations, reflections, or any combination of these)
Non-rigid transformations: shape distorted (vertical
and horizontal stretches and shrinks)
Do Worksheet
Do Exploration #1 on Pg. 138
October 07, 2009
Translations:
Horizontal:
Vertical:
f(x - c)
translate right c units
f(x + c)
translate left c units
f(x) + c
translate up c units
f(x) - c
translate down c units
October 07, 2009
The figure shows a graph of y = x3. Write an equation for
y2 and y3.
y2 =
3
y=x
y =
3
October 07, 2009
October 07, 2009
Reflections
Across the x-axis: y = -f(x)
Across the y-axis: y = f(-x)
October 07, 2009
Find an equation for the reflection of f(x) = 5x2 +x
across each axis.
across x-axis:
across y-axis:
October 07, 2009
October 07, 2009
Do Worksheet: Exploration 3
October 07, 2009
Stretches and Shrinks
Horizontal:
y=f
x
c
a stretch by a factor of c
a shrink by a factor of c
if c>1
if c<1
a stretch by a factor of c
a shrink by a factor of c
if c>1
if c<1
Vertical:
y = c f(x)
October 07, 2009
Find the equation for each of the following if
f(x) = x3 - 16x.
1. g(x) is a vertical stretch of f(x) by a factor of 3.
2. h(x) is a horizontal shrink of f(x) by factor of 1/2.
October 07, 2009
The graph of y = x2 undergoes the following
transformations, in order. Find the equation of the graph
that results.
* a horizontal shift 2 units to the right
* a vertical stretch by a factor of 3
* a vertical translation 5 units up
October 07, 2009
Determine the graph of the composite function
y = 2f(x+1) - 3 by describing the sequence of
transformations on the graph of y = f(x).
October 07, 2009
Graphing Absolute Value Compositions
Given the graph of y = f(x),
y = f(x)
reflect the portion of the graph below the
x-axis across the x-axis, leaving the
portion above the x-axis unchanged.
y = f( x ) replace the portion of the graph to the left
of the y-axis by a reflection of the portion
to the right of the y-axis across the y-axis,
leaving the portion to the right of the yaxis unchanged. (The result will show
even symmetry)
Graph f(x) = 5x3 + 2x
graph f(x)
graph f( x )
Do Worksheet: Exploration 2