SOLUTION: Describe the translation from y=x to y=3x+2

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Question 1183527: Describe the translation from y=x to y=3x+2
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52785)   (Show Source): You can put this solution on YOUR website!
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Describe the TRANSFORMATIONS from y=x to y=3x+2
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They are  NOT  translations:   they are  TRANSFORMATIONS ! 


First transformation is the stretching of the coordinate plane along the y-axis with the coefficient of 3,

and then the shift of 2 units up.



It is possible to express EQUIVALENTLY in other terms:  first is the compression along the x-axis 

with the coefficient of 3 and then the shift of 2 units up.

Solved and explained.


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When you answer such questions,  keep in your mind,  that the sequence of the transformations   DOES  MATTER.

For example,  in this case the stretching along  y-axis followed translation along y-axis
 IS  NOT  THE  SAME  as translation along  y-axis followed stretching along y-axis.


Keeping it in your mind,  re-consider the answer from  @MathLover1,  which is not precisely correct.



Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

In the equation , the is acting as the or of the identity function, shifted up or down .
When is negative, there is also a vertical reflection of the graph.
Notice in the figure below that multiplying the equation of
by the graph of by a factor of units if and the graph of f by a factor of units if . This means the larger the absolute value of , the steeper the slope.
in your case: the translation from to
graph is shifted up units
there is vertical stretch by a factor of units


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