Given:
The graph of the function [tex]f(x)=\dfrac{1}{x}[/tex].
To find:
The value of the function f(x), when x is close to zero.
Solution:
From the given graph it is clear that, f(x) approaches towards infinity and negative infinity as x approaches towards 0.
[tex]f(x)\to \infty[/tex] as [tex]x\to 0^+[/tex]
[tex]f(x)\to -\infty[/tex] as [tex]x\to 0^-[/tex]
In means, the value of must be very large positive value or very large negative if x is close to zero.
From the given options -10,000 is very large negative value.
So, the possible value of f(x) could be -10000 if x is close to 0.
Therefore, the correct option is A.
