The given function is [tex]y= \sqrt{25x-75}+3 [/tex]
The parent function of the given function is [tex] \sqrt{x} [/tex]
So, the given function will be written as following :
[tex]y= \sqrt{25x-75}+3 [/tex] ⇒⇒ add (-3) to both sides
[tex]y-3= \sqrt{25(x-3)} [/tex] ⇒⇒ take 25 as common from 25x and 75
[tex]y-3= \sqrt{25} \sqrt{(x-3)} [/tex] ⇒⇒ bring 25 outside the square root
[tex] y-3= \ 5 \sqrt{(x-3)} [/tex]
[tex] y = \ 5 \sqrt{(x-3)} +3 [/tex]
So, the given function can be graphed easily from the parent function √x
By translation √x from (0,0) to point (3,3), then dilated with factor 5
See the attached figure
Parent function √x ⇒⇒⇒ with blue color
The given function ⇒⇒⇒ with red color
So, The answer is [tex] y = \ 5 \sqrt{(x-3)} +3 [/tex]
