Question

The function f(x) = One-sixth (two-fifths) Superscript x is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)? (negative 3, StartFraction 4 Over 375 EndFraction) (negative 2, StartFraction 25 Over 24 EndFraction) (2, StartFraction 2 Over 75 EndFraction) (3, negative StartFraction 125 Over 48 EndFraction)

Answer 1

The ordered pair (-3 , $\frac{4}{375}$ ) is on g(x) ⇒ 1st 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)  (change the sign of y)
• If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)  (change the sign of x)

∵ $f(x)=\frac{1}{6}(\frac{2}{5})^{x}$

∵ f(x) is reflected across the y-axis to create the function g(x)

- Change the sign of x

∴ $g(x)=\frac{1}{6}(\frac{2}{5})^{-x}$

To find the point that lies on g(x) substitute x in g(x) by the x-coordinate of the point if the answer equal to the y-coordinate of the point, then the point lies on it if not then the point does not lie on it

∵ The coordinates of the point are (-3 , $\frac{4}{375}$ )

∴ x = -3 and y = $\frac{4}{375}$

- Substitute x by -3 in g(x)

∵ $g(x)=\frac{1}{6}(\frac{2}{5})^{-x}$

∴ $g(x)=\frac{1}{6}(\frac{2}{5})^{-(-3)}$

∴ $g(x)=\frac{1}{6}(\frac{2}{5})^{3}$

∵ $(\frac{2}{5})^{3}=\frac{2^{3}}{5^{3}}=\frac{8}{125}$

∴ $g(x)=\frac{1}{6}(\frac{8}{125})$

∴ $g(x)=\frac{8}{750}$

- Divide up and down by 2

∴ $g(x)=\frac{4}{375}$

∵ The value of g(x) equal to the y-coordinate of the point

∴ The point (-3 , $\frac{4}{375}$ ) lies on g(x)

The ordered pair (-3 , $\frac{4}{375}$ ) is on g(x)

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Answer 2

Answer:

A.

Step-by-step explanation:

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