Question 1188374
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Let f(x)=−3x. The graph of f(x)​is transformed into the graph of g(x) by a vertical stretch 
of 4 units and a translation of 4 units right. What is the equation for g(x)?
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<pre>
The new function g(x) is


    g(x) = 4*f(x-4) = 4*(-3(x-4)) = -12*(x-4).      <U>ANSWER</U>


I multiply f(x) by 4 to provide vertical stretch of 4 units, and I replace the argument "x" of the function f(x)

by (x-4) to translate the plot 4 units right.
</pre>

Solved and explained.



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<U>comment from student</U> : Thank you! One question. Since it's translating to 
the right, wouldn't it be -12 (x+4) though ?



<U>My response</U> :  &nbsp;&nbsp;NO.



It is a common &nbsp;<U>MISTAKE</U>&nbsp; to think that moving plot &nbsp;4 &nbsp;units right requires using &nbsp;(x+4)

instead of &nbsp;x.  &nbsp;&nbsp;With such level of knowledge the &nbsp;LOW &nbsp;SCORE &nbsp;is &nbsp;GUARANTEED.



The correct rule is &nbsp;EXACTLY &nbsp;as it is stated in my post.



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To see many other similar and different problems solved, &nbsp;look into the lesson 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/HOW-TO-write-functions-for-transformed-plots.lesson>HOW TO write functions for transformed plots</A> 

in this site.


Learn the subject from there . . .