**Educational Content: Rational Function Graph Analysis****Graph Description:**The graph displays a rational function. It has two distinct branches: one in the first quadrant and one in the third quadrant, both approaching but never touching the axes. - The vertical asymptote is at \( x = 0 \).- The horizontal asymptote is at \( y = 1 \).The graph suggests that as \( x \) approaches zero from the positive side, \( y \) increases without bound, and as \( x \) approaches zero from the negative side, \( y \) decreases without bound. As \( x \) moves towards positive or negative infinity, \( y \) approaches 1.**Problem Statement:**Decide which of the rational functions might have the given graph.**Options:**- **A.** \( f(x) = 1 + \frac{1}{x} \)- **B.** \( f(x) = 1 - \frac{1}{x} \) (Correct Answer)- **C.** \( f(x) = 1 - x \)- **D.** \( f(x) = \frac{1}{x} - 1 \)**Explanation:**Option **B**, \( f(x) = 1 - \frac{1}{x} \), correctly models the behavior of the graph. The function has a vertical asymptote at \( x = 0 \) and a horizontal asymptote at \( y = 1 \), matching the observed characteristics.

In the graph given, it can be observed that- At x =1, function f(x)=0 As x→ +infinity, function f(x)→1 x→ - infinity, function f(x)→1 x→ 0+, function f(x)→-infinity x→ 0-, function f(x)→+ infinityAll the above observation is fulfilled by- F(x)=1-1/X So, option (b) is correct