On a coordinate plane, 2 exponential functions are shown. Function f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 0.5) and goes through (1, 4). Function g (x) approaches y = 0 in quadrant 3 and decreases into quadrant 4. It crosses the y-axis at (0, negative 0.5) and goes through (1, negative 4). Which function represents g(x), a reflection of f(x) = Two-fifths (10)x across the x-axis? g(x) = Negative two-fifths(10)x g(x) = Negative two-fifths (one-tenth) Superscript x g(x) = Two-fifths (one-tenth) Superscript negative x g(x) = Two-fifths(10)-x

g(x)=1/2(3-x)

Its a lot of numbers but once you get into it and just start remembering the equations and numbers it goes smoother.

g(x) = Negative two-fifths(10)x

Step-by-step explanation:

In order to reflect a function over the x-axis, you have to multiply the function by minus one.

Given the function:

f(x) = 2/5(10)^x

Its reflection over the x-axis is:

-f(x) = -2/5(10)^x = g(x)

The correct option is;

g(x) = Negative two-fifths(10)x

Step-by-step explanation:

The rule for the reflection across the x-axis is as follows;

Reflection about the x-axis

Pre-image point before reflection = (x, y)

Point of image after reflection = ((x, -y)

Therefore, the x coordinate remains the same while the y coordinate changes sign

For which given that f(x) = y = 2/5(10)x and g(x) = Reflection of f(x) across the x-axis, we have

Reflection about the x-axis

Pre-image point before reflection = (x, f(x))

Point of image after reflection = (x, g(x))

Hence g(x) = -f(x) = -2/5(10)x.