Answer:
The equation that represents the transformation function is:
[tex]y=-\sqrt{x}+2[/tex]
Step-by-step explanation:
We are given a parent function f(x) as:
[tex]f(x)=\sqrt{x}[/tex]
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
2)
[tex]y=\sqrt{-x}+2[/tex]
at x=4 , we have:
[tex]y=\sqrt{-4}+2[/tex]
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.
3)
[tex]y=\sqrt{-x}-2[/tex]
at x=4 , we have:
[tex]y=\sqrt{-4}-2[/tex]
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.
4)
[tex]y=-\sqrt{x}-2[/tex]
at x=4 , we have:
[tex]y=-\sqrt{4}-2\\\\y=-2-2\\\\y=-4\neq 0[/tex]
Hence, option (4) is incorrect.
1)
[tex]y=-\sqrt{x}+2[/tex]
at x=4 , we have:
[tex]y=-\sqrt{4}+2\\\\y=-2+2\\\\y=0[/tex]
Hence, option (1) is the correct answer.
