The graph of r(x)=2+ (x+1)/x-3 is graph (a).Therefore ,graph (a) is correct.
We can analyze the function to determine its key features, which will help us to identify the correct graph.
Key features of r(x)
Vertical asymptotes: The function has vertical asymptotes at x=-3 and x=3.
This is because the denominator of the function is zero at these points.
Horizontal asymptote: The function has a horizontal asymptote at y=2.
This is because as x goes to positive or negative infinity, the x+1 term in the numerator becomes negligible compared to the x-3 term.
End behavior: As x approaches positive or negative infinity, the function approaches 2.
Analyzing the graphs
Graph (a) has vertical asymptotes at x=-3 and x=3, and a horizontal asymptote at y=2.
It also approaches 2 as x approaches positive or negative infinity. Therefore, graph (a) is the graph of r(x).
Graphs (b), (c), and (d) do not have the correct key features. Therefore, they cannot be the graph of r(x).
Question
. Which figure below is a graph of r(x)=2+ (x+1)/x-3 ？ a. b. c, d.