Translation

Question

Many transformations have equivalent transformations which produce the same graph. For instance, the line f(x)=2x can be translated up 4 units to go g(x)=2x(x+2)=2x+4. For the following equations find an equivalent transformation and prove using algebra that it is equivalent; that it produces the same graph. f(x)=x²; vertical stretch by a factor of 4 and f(x)=2^x; vertical stretch by a factor of 8.

Answer 1

f(X) = X²

 

Stretch factor of 4 would look like:

 

g(X) = 4X²

 

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given:  h(X) = X²/3

 

then:   p(X) = 12(X²/3)

 

                   = 4X²

 

vertically stretching the original function h(X) 

by a factor of 12 resulted in g(X) = 4x²

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f(X) = 2^x

 

vertical stretch by factor of 8 results in

 

        g(X) = 8 (2^x )

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Given:  h(X) = 2^x/6

 

vertically stretch by a factor of 48

 

           p(X) = 48 (2^x/6)

 

           p(X)  = 8(2^x)

 

This is the same as vertically stretching the 

problem function f(X)  by 8