Which function represents g(x), a reflection of f(x) = 4(one-half) superscript x across the x-axis?

g(x) = −4(2)x
g(x) = 4(2)−x
g(x) = −4(one-half) superscript x
g(x) = 4(one-half) superscript negative x

Step-by-step explanation:

we have

we know that

The rule of the reflection across the x-axis is

(x,f(x)) ------> (x,-f(x))

therefore

g(x) = −4(one-half) Superscript x

see the attached figure to better understand the problem

Step-by-step explanation:

we have

we know that

The rule of the reflection across the x-axis is

(x,f(x)) > (x,-f(x))

therefore

g(x) = −4(one-half) Superscript x

see the attached figure to better understand the problem

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)