Question

Describe how to obtain the graph of f(x)=x+1−−−−−√−2 by transforming the parent graph of f(x) =x√ .

Answer 1

Answer: Shift the graph two units down and left one unit.

Step-by-step explanation:

Here the parent function,

$f(x) = \sqrt{x}$

When the function is shifted left by a factor a then the new function is,

$f(x) = \sqrt{x+a}$

While when the function is shifted right by a factor A then new function,

$f(x) = \sqrt{x-a}$

Since here the transformed function is,  $f(x) = \sqrt{x+1} - 2$

Therefore it was obtained by shifting 1 unit towards left,

Now, when the parent function is shifted vertically upward by a factor a,

Then the new function is, $f(x) = \sqrt{x}+a$

While, when the parent function is shifted vertically downward by a factor a,

Then the new function is, $f(x) = \sqrt{x}-a$

Here, the transformed function is,  $f(x) = \sqrt{x+1} - 2$,

Therefore, it was obtained by shifting 2 unit downward.

Hence, Third Option is correct.