Sure, let us closely examine the function and understand what the graph would look like.
Given the function:
[tex]\[
f(n) = \sqrt[8]{2-2}
\][/tex]
First, simplify the expression inside the root:
[tex]\[
2 - 2 = 0
\][/tex]
Now the function becomes:
[tex]\[
f(n) = \sqrt[8]{0}
\][/tex]
Since the 8th root of 0 is 0, we can further simplify:
[tex]\[
f(n) = 0
\][/tex]
Therefore, for any value of [tex]\( n \)[/tex], [tex]\( f(n) \)[/tex] will always be [tex]\( 0 \)[/tex].
Graphically, this is represented by a horizontal line at [tex]\( y = 0 \)[/tex]. This means every point on this graph has a y-coordinate of 0, irrespective of the x-coordinate.
So, the correct representation of this function would be a horizontal line intersecting the y-axis at 0. Scanning through the given options with this in mind, the correct choice would be the one depicting a horizontal line along the x-axis.
Since not all the options are clearly provided in the query, here you should match this explanation with the correct provided graph option. For instance, if option A depicts a horizontal line at [tex]\( y = 0 \)[/tex], then A is the correct answer.
