MATH SOLVE

3 months ago

Q:
# 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)

Accepted Solution

A:

The ordered pair (-3 , [tex]\frac{4}{375}[/tex] ) is on g(x) ⇒ 1st answerStep-by-step explanation:Let us revise the reflection across the axesIf 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)∵ [tex]f(x)=\frac{1}{6}(\frac{2}{5})^{x}[/tex]∵ f(x) is reflected across the y-axis to create the function g(x) - Change the sign of x∴ [tex]g(x)=\frac{1}{6}(\frac{2}{5})^{-x}[/tex]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 , [tex]\frac{4}{375}[/tex] )∴ x = -3 and y = [tex]\frac{4}{375}[/tex]- Substitute x by -3 in g(x)∵ [tex]g(x)=\frac{1}{6}(\frac{2}{5})^{-x}[/tex]∴ [tex]g(x)=\frac{1}{6}(\frac{2}{5})^{-(-3)}[/tex]∴ [tex]g(x)=\frac{1}{6}(\frac{2}{5})^{3}[/tex]∵ [tex](\frac{2}{5})^{3}=\frac{2^{3}}{5^{3}}=\frac{8}{125}[/tex]∴ [tex]g(x)=\frac{1}{6}(\frac{8}{125})[/tex]∴ [tex]g(x)=\frac{8}{750}[/tex]- Divide up and down by 2∴ [tex]g(x)=\frac{4}{375}[/tex]∵ The value of g(x) equal to the y-coordinate of the point∴ The point (-3 , [tex]\frac{4}{375}[/tex] ) lies on g(x)The ordered pair (-3 , [tex]\frac{4}{375}[/tex] ) is on g(x)Learn more:You can learn more about the reflection in brainly.com/question/5017530#LearnwithBrainly