Graphing a shifted and stretched absolute value function

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Graphing a shifted and stretched absolute value function
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My college algebra teacher took points off of everyone's exam because everyone transformed an absolute value function just like this. He insisted on instead writing it out as a piecewise function for every step, and his reasoning for that is because transforming an absolute value function like this because this is not able to handle more complicated functions, like nested fractions in the absolute value.

He did not take off points when we did quadratics like this, however.

DerekGreen
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Sir, Love you from India. You are doing a great job.

fundamentalsofphysicsnmath
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If you shift first and then multiply by 2, it would become a different function than the result.

Shiva-losq