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F(x)=2x^2 +5 what is transformation 1: and what is transformation 2:

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Question:

Describe the two transformations that were performed to go from


f(x)=x^2

to


f(x)=2x^2+5

Answer:

First, lets perform an horizontal shrink by a factor of 2 (Multiply the whole function by 2)


f(x)=x^2\rightarrow f(x)=2x^2

And then, let's move the function up by 5 units (add 5 to the whole function)


f(x)=2x^2\rightarrow f(x)=2x^2+5

Therefore, transformation one is an horizontal shrink by 2, and transformation two is a vertical displacement of +5 units.

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