Question

Which function represents g(x), a reflection of f(x) = 6(one-third) Superscript x across the y-axis?

Answer 1

The function $g(x)=6(3)^{x}$ represents a reflection of $f(x)=6(\frac{1}{3})^{x}$ across the y-axis ⇒ 3rd answer

Step-by-step explanation:

Let us revise the reflection across the axes

• If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
• If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

∵ $f(x)=6(\frac{1}{3})^{x}$

∵ 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

∴ $g(x)=6(\frac{1}{3})^{-x}$

∵ $(a)^{-n}=(\frac{1}{a})^{n}$

∵ $(\frac{1}{a})^{-n}=(a)^{n}$

∴ $(\frac{1}{3})^{-x}=(3)^{x}$

∴ $g(x)=6(3)^{x}$

The function $g(x)=6(3)^{x}$ represents a reflection of $f(x)=6(\frac{1}{3})^{x}$ across the y-axis

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You can learn more about reflection in brainly.com/question/5017530

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Answer 2

Answer:

b

Step-by-step explanation: