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.

assuming
\(g(x)=3 \sqrt{x-5}+7\)
and parent function is \(3 \sqrt{x}\)

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 Link

tardymanchester tardymanchester · Answer 2 · 2019-02-13T06:06:27-05:00

Answer:

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

Step-by-step explanation:

Given : Function \(g(x) = 3\sqrt{x-5}+7\)

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

Solution:

First we look the parent function of g(x)

The parent function of g(x) is \(3\sqrt{x}\)

Now, we see the transformations,

In \(g(x) = 3\sqrt{x-5}+7\)

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.