Translation and compression/expansion

[gillgill]

i have a question about translation and compression/expansion
y=√x ; y=√2x-5

how do u know u translate 5 units right first or horizontal compression by 1/2 first...?

 

[Link]

Y = 2(X^1/2) - 5

if i got that correct

 

[dextercioby]

Is that $y=\sqrt{2} x-5$ or $y=\sqrt{2x}-5$

??

Daniel.

 

[primarygun]

Exactly the same. There's no difference.
If it involves f(nx+m), then you need to beware of it.
If it involves nf(x)+m, no aware should be made.
In this case, since not the first case, no aware.

 

[Galileo]

If you simply replace x by x-5, the graph will be shifted 5 to the right.
If you replace x by 2x, you will horizontally compress the graph by a factor 2.

So, if you shift and then compress:
$$\sqrt{x} \rightarrow \sqrt{x-5} \rightarrow \sqrt{2x-5}$$

and if you compress and then shift:
$$\sqrt{x} \rightarrow \sqrt{2x} \rightarrow \sqrt{2(x-5)}$$

 

[gillgill]

o..icic...thx