The rules and what they mean:( )

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y f x

y af x

y f xa

y f bx

y f xb

y f x

y f x

This is our function

This is our function vertically stretched

This is our function vertically compressed

This is our function horizontally compressed

This is our function horizontally stretched

This is our function reflected over the x-axisThis is our function reflected over the y-axis

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y f x c

y f x c

y f x d

y f x d

This is our function with a horizontal shift rightThis is our function with a horizontal shift leftThis is our function with a vertical shift upThis is our function with a vertical shift down

That’s a lot of rules… Now what?!

Let’s apply the rules to move functions.y = 3x Let’s start with this functiony = 3x shift the function horizontally right 3horizontal movement will ALWAYS be inside with

the x added or subtracted and is OPPOSITE what you want.To move the function horizontally, place the

number inside parenthesis and do the opposite of the way you want to move. To move left put a plus and your number and to move right put a minus and your number.

y = 3(x – 3)

Let’s try some more!

y = 3x horizontal shift left 4

y = 3(x + 4)

y = 3x horizontal shift right 5

y = 3x horizontal shift left 7

y = 3(x - 5)

y = 3(x + 7)

But what about up and down?

y = 3x shift the function vertically up 5y = 3x + 5 just add on to the end.Remember up you need a + to move up and a – to move down. Vertical movements do EXACTLY what they say.y = 3x shift the function vertically down 2

y = 3x - 2

You try!

y = 3x vertical shift up 3

y = 3x vertical shift down 8y = 3x + 3

y = 3x - 8

Put them together!

y = 3x vertical shift down 5 and horizontal shift

right 6 y = 3(x – 6) – 5

Too easy? Let’s look at some others!Vertically stretch y = 3x by a scale factor of 2Simply put the 2 on the outside of 3x like this:

y = 2(3x)That’s it???? Yep, that’s it! But what if

it is a compression? Same deal but you will see a fraction.Try it! Vertically compress y = 3x by a scale factor of 1/4

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Horizontal compressions and stretches the number will be inside touching the x.

If the number is a whole number it will COMPRESSIf the number is a fraction it will STRETCH the function.y = 3x compress the function horizontally by a scale factor of 2

y = 3(2x)

y = 3x stretch the function horizontally by a scale factor of 1/2

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y x

y = 3x reflect across the x-axis

y = 3x reflect across the y-axis

y = 3(-x)

y = -3x