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**Prove It** I don't use a table of values when sketching trigonometric functions. I make sure to have a few different colours handy (like a 4 pen) and I sketch the "standard" sine graph. (blue)

Then I'd use a different colour to show the vertical dilation. (green)

Then I'd use a different colour to show the horizontal dilation. **(orange)**

Then I'd use a different colour again to show the horizontal translation. **(pink)**

And finally I'd use a different colour again to show the vertical translation. (purple)

Takes a while but you get a better understanding of the functions.