Question

Describe how to transform the graph of f into the graph of g.

f(x) = square root of quantity x minus eight. and g(x) = square root of quantity x plus four.

Answer 1

\[\sqrt{(x-8)}\]
\[\sqrt{(x+4)}\]

So in terms of add subtract, multiply divide, what is done to the x-8 part to make it become x + 4?

Answer 2

you divide by -2.

Answer 3

If you divided by -2 then the x would become -x/2, though.

Answer 4

No, -8 divided by -2, gives you 4. I might be wrong, but I inputted that into my calculator.

Answer 5

I know what you did, but this is what I'm saying:
\[\frac{ x-8 }{ -2 }= -\frac{ x }{ 2 }+4\]

Answer 6

Oh, okay.

Answer 7

Yeah. All you need to do is add 12. See why?

Answer 8

It is because you are just adding both 8 and 4? So, would my answer be Shift the graph of f right 12 units?

Answer 9

Nope. I just simply mean this: I want
x-8 to become
x+4 so...

x - 8
+ 12
--------
x + 4

Answer 10

Okay, now I get what you mean.

Answer 11

Yep :3 Now be careful. This is what a shift left and right is
(x - c)
x subtracted by some number. So if the form is x subtracted and we have (x+4), are you sure we're going right? :P

Answer 12

Left 4 units?

Answer 13

Yep. And this is why. If the form MUST be (x-c) and we have (x+4), this means what we actually have is (x-(-4)), which means left. So the graph, in total, was shifted left 12 units :3

Answer 14

Wait, my apologies, you are confusing me. First you said my answer, "left 4 units" was right, then you said in total, was shifted left 12 units. So which one is it?

Answer 15

Yeah, (x+4) is left 4 units. But in comparison to where we started, which was (x-8), we went a total of 12 units left.