Question

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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

Answer 1

f(x) = 5(1/5)-x
f(x) = 5(5)x

Answer 2

The function which represent the reflected function are $f(x) = 5(\frac{1}{5} )^{-x}$ and $f(x) = 5(5)^x$ .

What is reflection ?

Reflection is known as a flip of coordinates. It is a mirror image of the shape. If a figure is said to be a reflection of the other figure, then every point in the figure is at equidistant from each corresponding point in another figure.

We have,

The  $f(x) = 5(\frac{1}{5} )^x$  is reflected over the $y-$axis.

So,

When a function is flipped or reflected on $y-$axis then the coordinates at  $x-$axis changes its sign.

i.e. $(x,y)$ → $(-x,y)$

So, Using the above mentioned statement;

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

So, the function is reflected on $y-$axis, so, the $x$ coordinates will change to negative.

i.e.

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

So, this is the reflected function.

We know that a fraction with the negative power can be written as a reciprocal of the same fraction with the positive power.

i.e.

$(1/5)^{-x}= 5^x$

This means that the reflected function can also be written as,

$f(x) = 5(5)^x$.

Hence, we can say that the function which represent the reflected function are $f(x) = 5(\frac{1}{5} )^{-x}$ and $f(x) = 5(5)^x$ .

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