Question

Which function represents a reflection of f(x) = 5(0. 8)x across the x-axis? g(x) = 5(0. 8)–x g(x) = –5(0. 8)x g(x) = One-fifth(0. 8)x g(x) = 5(–0. 8)x.

Answer 1

The function which represents the reflection of provided function across the x-axis is,

$g(x) = -5(0. 8)x$

What is reflection of function?

The reflection of a function is flipping the original function with respect to a reference line.

The following steps used to for reflecting a the function-

• Select the function which has to be reflected.
• Select a baseline or reference line over which the function has to be reflected.
• Mark the corners of the function at the equidistant from the reference line as the original function has, but in the opposite direction.
• The reflected function is now is facing the opposite direction.

The function given in the problem is,

$f(x) = 5(0. 8)x$

The function has the positive sign. Therefore, this function is located in the first quadrant.Now this function is reflected across the x-axis. This will lead this function in the fourth quadrant, with negative sign.

Therefore, the function become,

$g(x) = -5(0. 8)x$

Hence, the function which represents the reflection of provided function across the x-axis is,

$g(x) = -5(0. 8)x$

Learn more about the reflection here;

brainly.com/question/1908648