October 17, 2012
(1.6) Graphical Transformations
1. Graph y = √x
Then graph the following and
describe how the graph
transformed.:
a. y = √x + 4 ___________
b. y = √x - 4 ___________
c. y = √(x+4) ___________
d. y = √(x-4) ___________
What happens to a function: y = f(x) when:
a. y = f(x) + c ___________________
b. y = f(x) - c ___________________
c. y = f(x + c) ___________________
d. y = f(x - c) ___________________
October 17, 2012
Graph y = √x
Then graph the following and
describe how the graph
transformed.:
a. y = - √x _____________
b. y = √(-x) ____________
What happens to a function y = f(x) when:
a. y = - f(x) ___________________
b. y = f(-x) ____________________
October 17, 2012
Graph y = √(4-x2)
Then graph the following and
describe how the graph
transformed.:
a. y = 2√(4-x2) _____________
b. y = 0.5√(4-x2) ___________
What happens to a function y = f(x) when y = c f(x) if:
a. c > 1 _______________________
b. 0 < c < 1 _____________________
October 17, 2012
Graph y = √(4-x2)
Then graph the following and
describe how the graph
transformed.:
a. y = √(4-(2x)2) ____________
b. y = √(4-(0.5x)2) ___________
What happens to a function y = f(x) when y = f(cx) if:
a. c > 1: _________________________
b. 0 < c < 1: _______________________
October 17, 2012
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
October 17, 2012
Translations:
Vertical:
f(x) + c
translate up c units
f(x) - c
translate down c units
Horizontal: f(x - c)
translate right c units
f(x + c)
translate left c units
October 17, 2012
The figure shows a graph of y = x3. Write an equation for
y2 and y3.
y = x3
y2 =
y3 =
October 17, 2012
Reflections
Across the x-axis: y = - f(x)
Across the y-axis: y = f(-x)
October 17, 2012
Find an equation for the reflection of f(x) = 5x2 +x
across each axis.
across x-axis:
across y-axis:
October 17, 2012
Stretches and Shrinks
Vertical:
y = c f(x)
a stretch by a factor of c if c>1
a shrink by a factor of c if c<1
Horizontal:
y=f x
c
a stretch by a factor of c if c>1
a shrink by a factor of c if c<1
October 17, 2012
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 17, 2012
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 17, 2012
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 17, 2012
October 17, 2012
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