Question

The function g(x) = 8(4x) is reflected across the x-axis to create f(x). What is the equation for f(x)? f(x) =_____ (4)x

Answer 1

Answer:

f(x) = -8(4)x

Step-by-step explanation:

The reflection of the point (x,y) across  the x-axis is the point (x,-y).

Having said this, to reflect the function y=g(x) = 8(4x) over the x-axis, we just need to evaluate the equation in the point: (x,-y).

y = 8(4x) ⇒ -y = 8(4x) ⇒ y = -8(4x)

Then f(x) = -8(4x)

Attached you will find the graph of g(x) (blue) and f(x) (red),

Answer 2

Answer:

$f (x) = -8(4x)$

Step-by-step explanation:

The transformation that reflects the function $g(x)$ on the axis is:

$y = -g (x)$.

Therefore if we have the function

$g (x) = 8 (4x)$ and we call $f (x)$ to the transformation that relieves g (x) on the x axis then:

$f (x) = -g (x)\\\\f (x) = -8(4x)$

Finally the equation for f(x) es:  $f (x) = -8(4x)$