Question

http://prntscr.com/20lsot

Answer 1

\[
y_1 = \sqrt{25x - 125} + 5 \\
y_1 = \sqrt{25x - 25 \cdot 5} + 5 = \sqrt{25 \cdot (x - 5)} +5 = \\
= \sqrt{25} \cdot \sqrt{(x - 5)} +5 = \color{blue}{ 5 \cdot \sqrt{x - 5} + 5} \\
\]
Now, we're asked to compare this to \(\color{green}{y_2 = 5 \cdot \sqrt{x}}\)
Let's see. at first we can see that \(y_1\) has a \(+5\) at the end, means all values are shifted up by 5.
Second, let's compare what's within the root itself. \( \sqrt{x-5} \) and \(\sqrt{x}\).
It shouldn't be hard to see, that the lowest possible value for \(\sqrt{x}\) is \(x = 0\), as our root can't be of negative number in here.
For \( \sqrt{x-5} \) that would be \(x = 5\) as \( \sqrt{5-5} = \sqrt{0} \).
This means that the \(y_1\) starts at \(x=5\) while \(y_2\) starts at \(x=0\). that shifts the graph 5 to the right.
Hope that's clear enough :S

Answer 2

thanks it does

Answer 3

Cool. wish I could explain it better. hehe.. too tired though