**As the options are missing, I will try to explain you how to find one**
Given function: f(x) = [tex]\frac{4}{x}[/tex]
If you plug in the value of x = 0, you will get:
f(x) = [tex]\frac{4}{0} = \infty[/tex]
If you approach from the right, the value of f(x) near x = 0 will be +[tex]\infty[/tex], whereas if you approach from the left, the value of f(x) near x = 0 will be -[tex]\infty[/tex]. It means that at x=0, there will be a discontinuity (as shown in only graph attached with the question.) If there is no discontinuity at x=0, you can ignore that option.
Now, if there are multiple graphs having discontinuity at x = 0, you can do the following step:
Plug in the value of x = 4 in the given function.
f(x) = [tex]\frac{4}{4} = 1[/tex]
It means that at x = 4, the value of y = f(x) will be +1.
Now Plug in the value of x = -4 in the given function.
f(x) = [tex]\frac{4}{-4} = -1[/tex]
It means that at x = 4, the value of y = f(x) will be -1.
Nutshell: The graph having the discontinuity at x = 0, and the y values to be +1 and -1 for x = +4 and x = -4 respectively, will be the correct option.
The graph of f(x) = [tex]\frac{4}{x}[/tex] is attached with the answer.
