Question

Choose the function whose graph is given by: (graph shown below)

Answer 1

Do you remember how a horizontal shift is applied? What it does to the x coordinate?

Answer 2

Let me look at my notes and see if I wrote down something like that >.<

Answer 3

The value of this function is 1 at x=1. Adding 1 to x has the effect of shifting the function left (or the y-axis to the right, whichever way you best remember). Subtracting 1 from x has the effect of shifting the function right (or the y-axis left).

Answer 4

Then it would be A?

Answer 5

As lars said, adding 1 to x would shift it to the left.
Is that what's happening in the picture? Or is it shifted to the right? :3

Answer 6

It's being shifted to the right. >.<

Answer 7

To shift, you do the opposite to your coordinate. That's how I like to remember it at least.
We want to shift in the positive direction? Ok we subtract.
We want to shift in the negative direction? Ok we add.

Answer 8

I'm writing that down hahah. xD
Okay, so now it would either be B or D, right?

Answer 9

Yes, B or D.

Answer 10

How do you narrow it down to whether it's the one with parenthesis or not?

Answer 11

\[\Large\rm y=\cos x\]So if I do this,\[\Large\rm y+1=\cos x\]And then subtract 1 from each side,\[\Large\rm y=\cos x-1\]Did I mess with the x or the y coordinate initially?

Answer 12

You moved the x and kept the y alone. So you messed with the x?

Answer 13

Nooo. :o
Look back at the first step I made.
I replaced y with y+1.
I messed with the y, yes?

Answer 14

In that case, yep you messed with the y. ;o

Answer 15

Messing with the y results in a `VERTICAL` shift. (Up or Down).

Answer 16

\[\Large\rm \color{orangered}{y}=\cos (x)\]If we had wanted to shift our function DOWN then this would have worked out nicely,\[\Large\rm \color{orangered}{y+1}=\cos (x)\]\[\Large\rm y=\cos(x)-1\qquad\leftarrow bad~:o\]

But instead:\[\Large\rm y=\cos (\color{orangered}{x})\]We want to mess with the x to make it shift to the right.\[\Large\rm y=\cos (\color{orangered}{x-1})\]

Answer 17

well shiz. That explains the parenthesis now.

Answer 18

lol

Answer 19

I think I got this (kinda) now I gotta remember this for the next time I mess with this quiz. ahah. -__-