Question

Identify the graph of f(x) = 3|x + 2|.
How would I do this?

Answer 1

Start with \(g(x) = |x|\). That is simple to graph, right?

Answer 2

Yes.

Answer 3

We can see \(g(x+2)=|x+2|\)

Answer 4

Do you know the relationship between \(g(x)\) and \(g(x+2)\)?

It is a translation.

Answer 5

Does it shift the graph up, down, left, or right?

Answer 6

....up??

Answer 7

Nope.

Answer 8

How do I figure out which way it goes?

Answer 9

Okay well, we know \(g(0) = |0| = 0\). Where does this point go after we translate?

Answer 10

On the origin, right?

Answer 11

Wait, no, nvm..

Answer 12

Well, we have the point \((0,0)\) but where is it put?

Answer 13

IDK. :(

Answer 14

http://www.purplemath.com/modules/fcntrans2.htm

Answer 15

So... to the right??

Answer 16

Oh wait, oops, wrong one, to the left.

Answer 17

Yep, it move to the left 2 units.

Answer 18

Oh...

Answer 19

f(x)=x
(x)=(x-2) moved 2 units to the right
f(x)=(x+2) moved 2 units to the left

Answer 20

so \(f(x)=3g(x+2)\). You need to figure out how the \(3\) changes the graph.

Answer 21

Oh, so how do I do that?

Answer 22

Well, the 3 should stretch the graph upwards.

Answer 23

Oh, okay, but if it was negative it would make it go down, right?

Answer 24

I know B and C are out.

Answer 25

Yep

Answer 26

Now, of A and D, which one stretches the graph upward more?

Answer 27

A

Answer 28

Nope. Actually A isn't stretched at all.

Answer 29

It's not?

Answer 30

no, if you look at it, the slope is 1 and -1. The slops should have changed to 3 and -3

Answer 31

the slope changes at the bottom of the V

Answer 32

Oh okay