1.6 Graphical Transformations Do Worksheet
1.6 Graphical Transformations Do Worksheet
1.6 Graphical Transformations Do Worksheet
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October 16, 2012<br />
<strong>1.6</strong> <strong>Graphical</strong> <strong>Transformations</strong><br />
functions that map real numbers to real numbers<br />
Rigid transformations: size and shape are unchanged<br />
(translations, reflections, or any combination of these)<br />
Non-rigid transformations: shape distorted (vertical<br />
and horizontal stretches and shrinks)<br />
<strong>Do</strong> <strong>Worksheet</strong>
October 16, 2012<br />
(<strong>1.6</strong>) <strong>Graphical</strong> <strong>Transformations</strong><br />
1. Graph y = √x<br />
Then graph the following and<br />
describe how the graph<br />
transformed.:<br />
a. y = √x + 4 ___________<br />
b. y = √x - 4 ___________<br />
c. y = √(x+4) ___________<br />
d. y = √(x-4) ___________<br />
What happens to a function: y = f(x) when:<br />
a. y = f(x) + c ___________________<br />
b. y = f(x) - c ___________________<br />
c. y = f(x + c) ___________________<br />
d. y = f(x - c) ___________________
October 16, 2012<br />
Graph y = √x<br />
Then graph the following and<br />
describe how the graph<br />
transformed.:<br />
a. y = - √x _____________<br />
b. y = √(-x) ____________<br />
What happens to a function y = f(x) when:<br />
a. y = - f(x) ___________________<br />
b. y = f(-x) ____________________
October 16, 2012<br />
Graph y = √(4-x 2 )<br />
Then graph the following and<br />
describe how the graph<br />
transformed.:<br />
a. y = 2√(4-x 2) _____________<br />
b. y = 0.5√(4-x 2 ) ___________<br />
What happens to a function y = f(x) when y = c f(x) if:<br />
a. c > 1 _______________________<br />
b. 0 < c < 1 _____________________
October 16, 2012<br />
Graph y = √(4-x 2 )<br />
Then graph the following and<br />
describe how the graph<br />
transformed.:<br />
a. y = √(4-(2x) 2 ) ____________<br />
b. y = √(4-(0.5x) 2 ) ___________<br />
What happens to a function y = f(x) when y = f(cx) if:<br />
a. c > 1: _________________________<br />
b. 0 < c < 1: _______________________
October 16, 2012<br />
Translations:<br />
Vertical: f(x) + c translate up c units<br />
f(x) - c<br />
translate down c units<br />
Horizontal: f(x - c) translate right c units<br />
translate left c units<br />
f(x + c)
October 16, 2012<br />
The figure shows a graph of y = x 3 . Write an equation for<br />
y 2 and y 3 .<br />
y = x 3<br />
y 2 = y 3 =
October 16, 2012<br />
Reflections<br />
Across the x-axis: y = - f(x)<br />
Across the y-axis: y = f(-x)
October 16, 2012<br />
Find an equation for the reflection of f(x) = 5x 2 +x<br />
across each axis.<br />
across x-axis:<br />
across y-axis:
October 16, 2012<br />
Stretches and Shrinks<br />
Vertical:<br />
y = c f(x)<br />
a stretch by a factor of c if c>1<br />
a shrink by a factor of c if c1<br />
c a shrink by a factor of c if c
October 16, 2012<br />
Find the equation for each of the following if<br />
f(x) = x 3 - 16x.<br />
1. g(x) is a vertical stretch of f(x) by a factor of 3.<br />
2. h(x) is a horizontal shrink of f(x) by factor of 1/2.
October 16, 2012<br />
The graph of y = x 2 undergoes the following<br />
transformations, in order. Find the equation of the graph<br />
that results.<br />
* a horizontal shift 2 units to the right<br />
* a vertical stretch by a factor of 3<br />
* a vertical translation 5 units up
Determine the graph of the composite function<br />
y = 2f(x+1) - 3 by describing the sequence of<br />
transformations on the graph of y = f(x).<br />
October 16, 2012
October 16, 2012<br />
Graphing Absolute Value Compositions<br />
Given the graph of y = f(x),<br />
y = f(x) reflect the portion of the graph below the<br />
x-axis across the x-axis, leaving the<br />
portion above the x-axis unchanged.<br />
y = f( x ) replace the portion of the graph to the left<br />
of the y-axis by a reflection of the portion<br />
to the right of the y-axis across the y-axis,<br />
leaving the portion to the right of the y-<br />
axis unchanged. (The result will show<br />
even symmetry)<br />
Graph f(x) = 5x 3 + 2x<br />
graph f(x)<br />
graph f( x )<br />
<strong>Do</strong> <strong>Worksheet</strong>: Exploration 2