Mathematics: The graph of y= sqrt of x is transformed as shown in the graph below. which equation represents the transformation function? graph and choices:

The graph of y= sqrt of x is transformed as shown

alyssabailey

03.01.2022

The equation that represents the transformation function is:

$y=-\sqrt{x}+2$

Step-by-step explanation:

We are given a parent function f(x) as:

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

Now, this function f(x) is transformed to get a function whose graph is given.

Let the transformed function is: g(x)

Clearly by looking at the graph we observe that at x=4 we have:

g(x)=0

$y=\sqrt{-x}+2$

at x=4 , we have:

$y=\sqrt{-4}+2$

As the term under the square root is negative hence, we will get the function's value as imaginary value and not real.

Hence, Option (2) is incorrect.

$y=\sqrt{-x}-2$

at x=4 , we have:

$y=\sqrt{-4}-2$

As the term under the square root is negative hence, we will get the function's value as imaginary value and not real.

Hence, Option (3) is incorrect.

$y=-\sqrt{x}-2$

at x=4 , we have:

$y=-\sqrt{4}-2\\\\y=-2-2\\\\y=-4\neq 0$

Hence, option (4) is incorrect.

$y=-\sqrt{x}+2$

at x=4 , we have:

$y=-\sqrt{4}+2\\\\y=-2+2\\\\y=0$

Hence, option (1) is the correct answer.

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