Some rules for translation of f(x) :

Some rules for translation of f(x) :

I think the way I prefer you can help you to solve the problems about the transformation more easily. I advise you not to just stay and look at what I’ve written! Use a paper and a pen and do the stages while you’re reading the article.Alright, let's startBefore doing anything specify some important points of the main function. Then the different stages:

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1. f(x)+a:

Just add the amount “a” to the “y” numbers (but don’t change the “x” numbers); x: ,-1 ,0 ,1, y: ,1+a ,0+a ,1+a,

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2. f(x+a)

Now, just add the amount of “-a” to the “x” numbers (but don’t change the “y” numbers); x: ,-1+(-a) ,0+(-a) ,1+(-a), y: ,1 ,0 ,1,

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3. a*f(x)

For this transformation, multiply the “y” numbers by “a” (don’t anything on “x” numbers); x: ,-1 ,0 ,1, y: ,1*a ,0*a ,1*a,

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4. f(a*x)

This time you should divide only the “x” numbers by “a”;x: ,-1/a ,0/a ,1/a,y: ,1 ,0 ,1,

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Now let’s combine all these rules: To transform the function “a f(b(x+c))+d”; 1.Set some points of f(x) x: ,p ,p’ ,p”, y: ,s ,s’ ,s”, 2.Multiply only the “y” numbers by “a” x: ,p ,p’ ,p”, y: ,S*a ,s’*a ,s”*a, 3.Divide only the “x” numbers by “b” x: ,p/b ,p'/b ,p"/b, y: ,S*a ,s’*a ,s”*a,

4.Add the amount of “-c” to only the “x” numbersx: ,p/b - c ,p'/b - c ,p"/b - c,y: ,S*a ,s’*a ,s”*a,5.Add the amount of “d” to only the “y” numbersx: ,p/b - c ,p'/b - c ,p"/b - c,y: ,(S*a)+d ,(s”*a)+d ,(s’*a)+d,

Abstract:

Now let’s solve a problem together

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And you just solved the problem (and certainly easily)! Good luck