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# Write a function g whose graph represents a vertical shrink by a factor of 1/2 of the graph of f(x)=2x+6.

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Write a function g whose graph represents a vertical shrink by a factor of 1/2 of the graph of f(x)=2x+6.

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Math High School
3 weeks
2023-01-14T17:32:28+00:00
2023-01-14T17:32:28+00:00 1 Answer
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Answer ( 1 )

functiong(x) which is a vertical shrink by afactorof 1/2 of thegraphof f(x) is equal tog(x)=x+4.5.## How does the transformation of a function happen?

transformationof a function mayinvolveany change.shifted horizontally(by transforming inputs) or vertically (bytransformingoutput), stretched (multiplying outputs or inputs), etc.original functionis y = f(x), assuming thehorizontalaxis is the input axis and the vertical is for outputs, then:Horizontalshift (also called phase shift):shiftby c units, y=f(x+c) (sameoutput, but c units earlier)Rightshift by c units, y=f(x-c)(same output, but c units late)VerticalshiftUpby d units: y = f(x) + dunits: y = f(x) – dStretching:Verticalstretch by a factor k: y = k × f(x)stretchby a factor k: y = f(x/k)graphof f(x)=2x+6 needed to bevertical shrinkby afactorof 1/2 is,functiong(x) which is a vertical shrink by afactorof 1/2 of thegraphof f(x) is equal tog(x)=x+4.5.Transforming functionshere: