Question

Which function represents the reflection over the x-axis of f(x) = StartRoot x EndRoot?

Answer 1

The function which represents the reflection over x-axis is the attached graph.

Step-by-step explanation:

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

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

$\begin{aligned}g(x) &=f(x) *-1 \\&=-f(x) \\g(x) &=-\sqrt{x}\end{aligned}$

For $x=0$⇒$g(x)=0$

For $x=1$⇒$g(x)=-1.41$

For $x=4$⇒$g(x)=-2$

Thus, the reflection of f(x) over x-axis is $g(x)=-\sqrt{x}$

Answer 2

Answer:

The last image is the right answer.

Step-by-step explanation:

The given function is

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

As you can notice the equation belongs to a radical function, which graph is half of a horizontal parabola.

The graph of this parent function is in the first quadrant. That means its reflection over the x-axis means it will move it to the fourth quadrant. In other words, to every positive x-value, there would be a negative y-value.

Therefore, the right answer is the last image, the second table, because it shows this pattern.