Transformations of Functions Given a parent function y = f(x), we can transform this function by applying parameters a, b,c and d to produce a new function g(x) = af(b(x – c)) + d. This new function will have the same basic shape of the original function but may be shifted, stretched/compressed, or reflected over a coordinate axis. For each transformation described below, write an inequality involving the appropriate parameter. The first one has been done for you. 1. _d >0__ translate d units up 2. translate . _units down 3. translate , units right translate , units left _vertical stretch by a factor of 5. 6. vertical compression by a factor of _ horizontal stretch by a factor of 7. 8. horizontal compression by a factor of . 9. reflection over the x-axis reflection over the y-axis 10. Which parameters affect the domatn of the original function y = f(x)? Which parameters affect the range of the original function y = f(x)? 4.
Transformations of Functions Given a parent function y = f(x), we can transform this function by applying parameters a, b,c and d to produce a new function g(x) = af(b(x – c)) + d. This new function will have the same basic shape of the original function but may be shifted, stretched/compressed, or reflected over a coordinate axis. For each transformation described below, write an inequality involving the appropriate parameter. The first one has been done for you. 1. _d >0__ translate d units up 2. translate . _units down 3. translate , units right translate , units left _vertical stretch by a factor of 5. 6. vertical compression by a factor of _ horizontal stretch by a factor of 7. 8. horizontal compression by a factor of . 9. reflection over the x-axis reflection over the y-axis 10. Which parameters affect the domatn of the original function y = f(x)? Which parameters affect the range of the original function y = f(x)? 4.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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
Transcribed Image Text:Transformations of Functions
Given a parent function y = f(x), we can transform this function by applying parameters
a, b, c and d to produce a new function g(x) = af (b(x – c)) + d. This new function will
have the same basic shape of the original function but may be shifted,
stretched/compressed, or reflected over a coordinate axis.
For each transformation described below, write an inequality involving the appropriate
parameter. The first one has been done for you.
1. _d > 0_ translate d units up
2.
translate
units down
3.
translate
units right
4.
translate
units left
vertical stretch by a factor of
5.
vertical compression by a factor of
6.
horizontal stretch by a factor of
7.
8.
horizontal compression by a factor of
9.
reflection over the x-axis
10.
reflection over the y-axis
Which parameters affect the domatn of the original function y = f(x)?
Which parameters affect the range of the original function y = f(x)?
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