Question

Select the graph of y = – |x + 3| + 2

Answer 1

Are you familiar with the graph of \(y=|x|\) ? :)
Our graph will be based off of it with just a few minor adjustments.

Answer 2

I've tried to grasp the basics of this lesson and I'm just having difficulty on picking it up, so I can't quite say I'm all too familiar with it, though I know what you are referring to.

Answer 3

Ok well it's a V shape. That's all we need to worry about for now :)
Transformations can be a little tricky.. we'll do our best to get through this though.

Answer 4

So here is y=|x|.

Answer 5

This is the graph of \(y=|x|+2\).
We have shifted the function up 2 units.

Answer 6

This is the graph of \(y=-|x|+2\).
The negative flips the function vertically.

Answer 7

Ignore the green V, that's just so we can compare it to the original.
The one we're looking at is the black line in each picture :)

Answer 8

And this is the graph of \(y=-|x+3|+2\).
It has been shifted 3 units to the left.

Answer 9

This is probably the hardest part, understanding why we shift it to the left when it's a +3.

Answer 10

And I'm not exactly sure of a good way to explain ittttt.
But umm I guess the idea is, whenever we are making a change to x, it will change the y value in the opposite way.

Answer 11

\[\large y=-|\color{orangered}{x}|+2 \qquad \rightarrow \qquad y=-|\color{orangered}{x+3}|+2\]This was a change we made to the x value. we replaced x with x+3.

Answer 12

I dunno, blah :3

Transformations can be tough.. I hope this helped a little bit at least D:

Answer 13

It did! Thank you very much, actually. I can actually visualize what's going on now, and it's certainly a lot less confusing. c: Thank you~

Answer 14

heh c: