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$y = x^n $ is transformed to $0.5(3x+2)^n - 1$. Describe the transformations.

Not too sure on this one, but I factorised $3x+2$ to $3(x+2/3)$, giving me a translation $-2/3$ to the left followed by a stretch scale factor $1/3$ parallel to x-axis. After that, it would be stretch scale factor $1/2$ parallel to y-axis followed by a translation 1 unit down.

This definitely doesn't seem right though. My only other thought would be to find the inverse of $3x+2$ which is $(x-2)/3$.

Cheers guys

2 Answers2

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Your first thought is correct.

See some of the related posts on this page for more practice in solving these types of problems.

Another helpful tool is a graphing calculator, which allows you to visualize easily transformations, which may in turn help you remember how they work.

user0
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Let assume wlog $n=2$ and analize the effect of the single terms.

  • $y=x^2 \to y=\frac12 x^2$ this is a streching in vertical direction (along $y$)

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  • $y=x^2 \to y=x^2-1$ this is a translation of $-1$ in vertical direction (along $y$)

enter image description here

  • $y=x^2 \to y=(3x+2)^2$ this is a translation of $-2/3$ in horizontal direction (along $x$) and a stretching of the function in horizontal direction

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and this is the final effect of the three transformation togheter

  • $y=x^2 \to y=\frac12(3x+2)^2-1$

enter image description here

Refer also to the related

user
  • 162,563