7.5 TRANSFORMATIONS

OBJECTIVE

• Review
• Review over how to graph functions
• Go over moving the graph horizontally
• Go over moving the graph vertically
• Go over expanding and shrinking the graph
• Now try some on your own
• Recap

Review

What’s a function?

A function is a relation with only one output for each input.

What’s function notation?

Function notation is usually written as a letter with parenthesis in front of it, and another letter inside those parenthesis.

How do we solve a function?

First, we take the function they gave us, second we either apply the number inside the parenthesis, or we solve the equation.

How do we graph function?

Plug in points for x, solve for y, and plot the points

Graphing functions

So we know the basics of a graph right?

But what if you’re asked to skew the graph some?

For example:

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But what if we want to skew this graph to the left three slots?

What about to the right 3 slots?

What about up 3 slots?

Down 3 slots?

SO HOW DO WE DO IT?

MOVING THE GRAPH UP

Let’s look at a quick x-y chart to see what this means.

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X Y

0

3

1

2

3

4

7

12

So what’s the graph look like?

MOVING THE GRAPH DOWN

0

-3

1

2

3

-2

1

6

SO WHAT OTHER WAYS CAN WE MOVE THE GRAPH?

So moving the graph up and down was pretty simple, but what about moving the graph left or right?

This gets a little more complicated, so let’s experiment.

First off, we know that y goes up and down, so adding or subtracting something from y is pretty easy.

However, x is the variable that determines left to right, and we can’t just add something to the equation because that’s how we move up and down.

So, any ideas?

Well, let’s just try a few things and see what happens

MOVING THE GRAPH HORIZONTALLY

MOVING THE GRAPH LEFT

-3

0

-2

-1

0

1

4

9

That was different.

So then, what’s the graph look like?

So, why did we pick -3 as our first point and not 0?

MOVING THE GRAPH TO THE RIGHT

3

0

2

1

0

1

4

9

It makes sense, so what does the graph look like?

So as we can see, it did shift to the right 3 slots.

But that’s weird, why is it that subtracting from x moves the graph to the right,

but adding moves it to the left?

It almost seems like it’s an inverse operation.

THE RULE FOR TRANSFORMING GRAPHS

SO, HOW DO WE MAKE THE GRAPH STRETCH OR SHRINK THEN?

There are actually a few more things we can do to the graph to change it (without actually changing the graph completely).

We can stretch the parabola, and we can constrict the parabola.

Stretching and constricting (shrinking) the parabola is a little harder to see than just moving it, so explaining how it works is going to be a little tougher.

It’ll be easier if we just dive in.

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SHRINKING A PARABOLA

0

0

1

2

3

2

8

18

So our graph changes from:

To:

SO HOW DO WE MAKE IT STRETCH?

STRETCHING A PARABOLA

0

0

2

4

6

2

8

18

Again, we went from this:

To this:

And that’s pretty much it

That’s how you transform graphs! �

So now it’s that time…

Recap