Answer:
Option 2 -Translate the parent function 5 units to the right and 7 units up.
Step-by-step explanation:
Given : Function [tex]g(x) = 3\sqrt{x-5}+7[/tex]
To find : Which describes how to graph [tex]g(x) = 3\sqrt{x-5}+7[/tex] by transforming the parent function?
Solution:
First we look the parent function of g(x)
The parent function of g(x) is [tex]3\sqrt{x}[/tex]
Now, we see the transformations,
In [tex]g(x) = 3\sqrt{x-5}+7[/tex]
7 unit is added in the function i.e,
If f(x)→f(x)+a then function is shifted upward by unit a
⇒ g(x)→g(x)+7 then function is shifted upward by unit 7
5 unit is subtracted in the value of x
If f(x)→f(x-b) then function is shifted right by unit b
⇒ g(x))→g(x-5) then function is shifted right by unit 5
Therefore, The translation in the parent function is 5 units right and 7 unit upward.
So,Option 2 is correct.
