Answer:
The function of the graph is f(x) = [tex]\frac{1}{3x^{5} }[/tex] .
Step-by-step explanation:
The answer can be found by examining the graph closely.
Let f(x) be the required function.
The graph shows that for positive values of 'x' the the value of 'y' is positive.
For negative values of 'x' the value of 'y' is negative.
Since, the value of 'y' is positive only when the values of 'x' are less than 1, it implies that the function is reciprocal.
Since, for all negative values of 'x' the values of 'y' are negative, it implies that the function has an odd power of 'x'.
If the function had an even power of 'x' , the values of 'y' would have been positive even for negative values of 'x'.
There are two options where the function has an odd power of 'x'.
They are f(x) = [tex]\frac{-1}{3x^{5} }[/tex] and f(x) = [tex]\frac{1}{3x^{5} }[/tex] .
If the function has negative sign, the values of f(x) will be positive even for negative values of 'x'.
But in the graph, it is not so.
So, the required function is f(x) = [tex]\frac{1}{3x^{5} }[/tex] .
