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Describe the translation from f ( x ) = I x I... to f ( x ) = - I x + 2 I + 12 . Select one: a. Steeper and left 2. b. Left 2, up 12, and opens downward. c. Left 2 and up 12. d. Right 2, up 12, and opens downward.

Describe the translation from f ( x ) = I x I... to f ( x ) = - I x + 2 I + 12 . Select one: a. Steeper and left 2. b. Left 2, up 12, and opens downward. c. Left 2 and up 12. d. Right 2, up 12, and opens downward.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

Describe the translation from f ( x ) = I x I... to f ( x ) = - I x + 2 I + 12 .

Select one:
a.

Steeper and left 2.

b.

Left 2, up 12, and opens downward.

c.

Left 2 and up 12.

d.

Right 2, up 12, and opens downward.

Expert Solution
Step 1

Transformation of the function y=f(x)

Function

Transformation
f(x)+d vertical translation upwards d units 
f(x)-d vertical translation downwards d units 

f(x+c)

 Horizontal translation left c units 
f(x-c) Horizontal translation right c units
f(-x) Reflection over y axis
-f(x) Reflection over x-axis
f(bx)
  • for |b|>0 horizontal compression 
  • for 0<|b|<1 horizontal Stretch
bf(x)
  • for |b|>0 vertical Stretch 
  • for0<|b|<1 vertical  compression

 

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