Range is wrong **Understanding Rational Function Characteristics****Graph Analysis of Rational Functions**The graph of a rational function $ f $ is shown. This graph is complete and contains no "holes."**Task: Use the graph to solve the following.****(a) Intercepts Identification**- **x-intercepts (where the graph crosses the x-axis):** Options: 1, -1, -4, None- **y-intercepts (where the graph crosses the y-axis):** Options: -4, 4, 1, None**(b) Asymptotes Calculation**- **Vertical Asymptotes (lines the graph approaches but never touches):** Enter the equation(s) as needed. In this case: $ x = 4 $.- **Horizontal Asymptotes (horizontal line the graph approaches as $ x $ extends to infinity):** In this context: $ y = 1 $.**(c) Domain and Range Determination**- **Domain (set of all possible x-values):** $ (-\infty, 1) \cup (1, \infty) $- **Range (set of all possible y-values):** $ (-\infty, 0) \cup (0, \infty) $**Graph Description:** The graph features a hyperbola with two distinct branches, one in the second quadrant approaching the vertical line $ x = 4 $ from below and the horizontal line $ y = 1 $ from above, and the other branch in the first quadrant, following similar behavior but in the opposite direction. The asymptotes serve as boundaries that the graph approaches but never crosses.**Practice Verification**Use this information to check understanding of intercepts and asymptotes in rational functions.

For a function y=f(x), the set of real values of x for which f(x) is defined is called the domain of the function. For a function, y=f(x), the set of all the real values of y that results corresponding to the real values of x is the range of f(x).A graph intersects the x axis at the x-intercept and the y axis at the y-intercept. From the graph, it can be observed that the graph intersects the x axis at -1, 0 and the y axis at 0, -4. Hence, the x-intercept is -1and the x-intercept is -4. The only point of intersection on the x axis is -1, 0, hence, select the option -1 for the first option. The only point of intersection on the y axis is 0, -4, hence, select the option -4 for the second option.The distance between the line, x=1 and the curve approaches 0 ,when y→∞. Hence, the vertical asymptote is x=1. The distance between the line, y=4 and the curve approaches 0, when x→∞. Hence, the horizontal asymptote is y=4. Therefore, fill the first blank by x=1 and the second blank by y=4.From the graph, it can be observed that: The domain of the graph is -∞,1∪1, ∞. The range of the graph is -∞, 4∪4, ∞. The first blank is correctly filled, fill the second blank by -∞, 4∪4, ∞.