The ordered pair (-3 , [tex]\frac{4}{375}[/tex] ) 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)
∵ [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
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