Question

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
Answer....C g(x) = −4(one-half) Superscript x

Answer 1

Option C will be correct.

Explanation:

If a function y = f(x) is reflected across the x-axis, then the equation of the reflected function will be a new function y = - f(x) = g(x).

Therefore, on reflection across the x-axis, the y-values of the function just alter its sign corresponding to the same x-values.

Now, the given function is
`f(x) = 4((1)/(2) )^(x)`.

Therefore, on reflection across the x-axis it will generate a new function i.e.
`g(x) = - 4((1)/(2) )^(x)`

Therefore, option C will be correct. (Answer)