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The function f(x) = 5(1/5)^x is reflected over the y-axis. Which equations represent the reflected function? Check all that apply.


f(x) =1/5 (5)x
f(x) =1/5 (5)^–x
f(x) =1//5 (1/5)^x
f(x) = 5(1/5)^–x
f(x) = 5(5)^x
f(x) = 5(5)^–x

Respuesta :

amberharris0527

Just the test, D and E are correct:  

f(x)= 5([tex]\frac{1}{5}[/tex])[tex]^{-x}[/tex]

f(x)= 5(5)[tex]^{x}[/tex]

xero099

Answer:

[tex]f(x) = 5\cdot \left(\frac{1}{5}\right)^{-x}[/tex] and [tex]f(x) = 5\cdot 5^{x}[/tex]

Step-by-step explanation:

A reflected function means that each value of the original function can be obtained by using a value of x that has the same distance to the symmetry axis than original value of x. That is:

[tex]y = f (L - x) = f (L + x)[/tex]

Since [tex]L = 0[/tex], reflected function has the following form:

[tex]f(-x) = 5\cdot \left(\frac{1}{5}\right)^{-x} = 5 \cdot \left[\left(\frac{1}{5} \right)^{x} \right]^{-1} = 5\cdot 5^{x} = 5^{1+x}[/tex]

Hence, correct options are:

[tex]f(x) = 5\cdot \left(\frac{1}{5}\right)^{-x}[/tex] and [tex]f(x) = 5\cdot 5^{x}[/tex]

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