The function [tex]g(x)=6(3)^{x}[/tex] represents a reflection of [tex]f(x)=6(\frac{1}{3})^{x}[/tex] across the y-axis ⇒ 3rd answer
Step-by-step explanation:
Let us revise the reflection across the axes
∵ [tex]f(x)=6(\frac{1}{3})^{x}[/tex]
∵ g(x) is the image of f(x) after reflection across the y-axis
- From the rule above reflection across the y-axis changes the sign of x
∴ [tex]g(x)=6(\frac{1}{3})^{-x}[/tex]
∵ [tex](a)^{-n}=(\frac{1}{a})^{n}[/tex]
∵ [tex](\frac{1}{a})^{-n}=(a)^{n}[/tex]
∴ [tex](\frac{1}{3})^{-x}=(3)^{x}[/tex]
∴ [tex]g(x)=6(3)^{x}[/tex]
The function [tex]g(x)=6(3)^{x}[/tex] represents a reflection of [tex]f(x)=6(\frac{1}{3})^{x}[/tex] across the y-axis
Learn more:
You can learn more about reflection in brainly.com/question/5017530
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