14.11.2014 Views

1.6 Graphical Transformations Do Worksheet

1.6 Graphical Transformations Do Worksheet

1.6 Graphical Transformations Do Worksheet

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

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

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!