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# 4 – Transforming Functions

• How would you un-bake a cookie? Could you un-burn a candle? Unless you have a time machine, some things in life can’t be reversed.
• However, if you can represent a relationship with an equation, then it becomes relatively easy flip the mathematical model around and do all sorts of otherwise impossible things, like control time or unburn a candle.
• Maybe you have a cat. Maybe you have a dog. Both animals come in all kinds of shapes and sizes, but no matter how you dress them up, you can always tell which is a cat and which is a dog. You’ll see that functions behave in much the same way.
• With a little arithmetic you’ll see how to raise the graphs of functions up or lower them down. You’ll see how to stretch the shape of a function vertically or horizontally, how to shift them from side to side, or even flip them around.
• In this unit, you’ll learn to transform a variety of functions. Even though they belong to different families, you’ll see patterns emerge, and you will be able to predict how a function will change even before you graph it.

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