Transformations of a Function af(x-h)+k

Hello there! Today's video will be about the different transformations you can do to a function. The original function which I will refer to as the reference function or the parent function is f(x). In this video, there will be 3 different variables mentioned: a, h, and k.

a is the number in front of the function that we multiply by. This number tells us whether or not the function is flipped and whether the function is compressed or stretched. If a is negative, this means the function is flipped. If a is positive, this means the function keeps its original orientation. If a is less than 1, this means the function is compressed. If a is greater than 1, this means the function is stretched.

h is the number that appears inside the parenthesis coupled with x. This number tells us the horizontal shift or translation of the function (left or right). If you see x+h, this means h is a negative number so there is a horizontal shift to the left. If you see x-h, this means h is a positive number so there is a horizontal shift to the right.

k is the number that appears outside of the parenthesis. This number tells us the vertical shift or translation of the function (up or down). If k is positive, this means there is a vertical shift upwards. If k is negative, this means there is a vertical shift downwards.

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