Question

Describe the transformation f(x) = √x + 1 − 5 in words. The parent function f(x) = √x has been shifted 1 unit and 5 units.

Answer 1

Answer:

The translation is $1$ unit to the left and $5$ units down

Step-by-step explanation:

we have

$g(x)=\sqrt{x+1}-5$

$f(x)=\sqrt{x}$ -----> parent function

we know that

The transformation

f(x)-----> g(x) has the following rule

$(x,y)-------> (x-1,y-5)$

That means

The translation is $1$ unit to the left and $5$ units down

see the attached figure to better understand the problem

Answer 2

Answer:

We are given,

The transformed function is $f(x)=\sqrt{x+1}-5$.

So, we can see that,

The parent function is $f(x)=\sqrt{x}$.

Then, we have,

The parent function is translated 1 units to the left to give $\sqrt{x+1}$.

Then, it is translated 5 units downwards to give the function  $\sqrt{x+1}-5$.

Hence, we have,

The parent function $f(x)=\sqrt{x}$ is translated 1 unit to the left and 5 units down.