The function which represents the reflection over x-axis is the attached graph.
Step-by-step explanation:
Given that [tex]f(x)=\sqrt{x}[/tex]
To reflect a function over x-axis, we need to multiply the function by -1.
Thus, to reflect f(x) over x-axis, multiply f(x) by -1.
Thus, the new function g(x) is given by
[tex]\begin{aligned}g(x) &=f(x) *-1 \\&=-f(x) \\g(x) &=-\sqrt{x}\end{aligned}[/tex]
For [tex]x=0[/tex]⇒[tex]g(x)=0[/tex]
For [tex]x=1[/tex]⇒[tex]g(x)=-1.41[/tex]
For [tex]x=4[/tex]⇒[tex]g(x)=-2[/tex]
Thus, the reflection of f(x) over x-axis is [tex]g(x)=-\sqrt{x}[/tex]
