Question

Which graph represents the function f(x)=4 / x

Answer 1

Answer:

All functions of the form f (x) = a / x are known as reciprocal functions.

Where a is a real number

The graph of f (x) is a hyperbola with domain (-infinity, 0) U (0, infinite)

The graph of the function f (x) = 4 / x has a horizontal asymptote at y = 0 and a vertical asymptote at x = 0

As x approaches infinity y approaches 0

As x approaches 0, y approaches infinity.

The graph of this function is shown in the attached figure.

Answer 2

Answer: The graph of rectangular hyperbola represents the function f(x)=4/x.

Explanation: given function, f(x)= 4/x.

The above function shows equation of rectangular hyperbola or equilateral hyberbola.(because, it is the type of $xy=c^2$.)

Thus, the asymptote  of the given function must be perpendicular.

Moreover, if x=2, y=2, if x=-2, y=-2

                 If x=4, y=1, if x=-4, y=-1

Therefore, this hyperbola is passing through points (2,2), (-2,-2), (4,1) and (-4,-1).