Which function represents the reflection over the x-axis of f(x) = startroot x endroot?

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

Step-by-step explanation:

Given that

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

For ⇒

For ⇒

For ⇒

Thus, the reflection of f(x) over x-axis is

Step-by-step explanation:

The given function is

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.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2