Question

Which describes how to graph g(x) = 3√x-5+7 by transforming the parent function?

Translate the parent function 5 units to the left and 7 units up.
Translate the parent function 5 units to the right and 7 units up.
Translate the parent function 5 units down and 7 units to the right.
Translate the parent function 5 units up and 7 units to the right.

Answer 1

assuming

`g(x)=3 √(x-5)+7`
and parent function is
`3 √(x)`


to move a function up c units, add c to whole function
to move a function to right c units, minus c from every x

7 was added to whole function and 5was mnused from every x

moved 7 up and 5 to right

2nd option

Answer 2

Option 2 -Translate the parent function 5 units to the right and 7 units up.

Explanation:

Given : Function
`g(x) = 3√(x-5)+7`

To find : Which describes how to graph
`g(x) = 3√(x-5)+7` by transforming the parent function?

Solution:

First we look the parent function of g(x)

The parent function of g(x) is
`3√(x)`

Now, we see the transformations,

In
`g(x) = 3√(x-5)+7`

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.