Question

Please Help!!

Answer 1

Just the test, D and E are correct:  

f(x)= 5($\frac{1}{5}$)$^{-x}$

f(x)= 5(5)$^{x}$

Answer 2

Answer:

$f(x) = 5\cdot \left(\frac{1}{5}\right)^{-x}$ and $f(x) = 5\cdot 5^{x}$

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:

$y = f (L - x) = f (L + x)$

Since $L = 0$, reflected function has the following form:

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

Hence, correct options are:

$f(x) = 5\cdot \left(\frac{1}{5}\right)^{-x}$ and $f(x) = 5\cdot 5^{x}$