Question

which function represents g(x), a reflection of f(x) = (2/5)(10)^x across the x-axis?
options:
g(x) = -2/5 (10)^x
g(x) = -2/5 (1/10)^x
g(x) = 2/5 (1/10)^{-x}
g(x) = 2/5 (10)^{-x}

Explanation:

Step1: Recall reflection rule

Reflecting a function \( f(x) \) across the \( x \)-axis changes \( f(x) \) to \( -f(x) \).

Step2: Apply rule to \( f(x) \)

Given \( f(x)=\frac{2}{5}(10)^x \), reflecting across \( x \)-axis gives \( g(x)=-f(x)=-\frac{2}{5}(10)^x \).

Answer:

\( g(x) = -\frac{2}{5}(10)^x \) (the first option among the given choices)