Oet Help / Oet Started Select all statements that correctly compare the graph of \( g \) with the graph of \( f(x)=\frac{1}{x} \). The graphs have the same asymptotes. The graphs have different asymptotes. The graphs have the same domain and range. The graphs have different domains and ranges. The graph of \( g \) lies closer to the axes than the graph of \( f \). The graph of \( g \) lies farther from the axes than the graph of \( f \). Both graphs are in the first and third quadrants. The graph of \( g \) is in the second and fourth quadrants, while the graph of \( f \) is in the first and third quadrants. Previous 1 2 3 4 5 6 7 8 9 10 Next Live Tutor

We’ll show that if you start with f(x) = 1/x and let g be the reflection of f in the x‐axis, then g(x) = –1/x. (Any nonzero constant multiple of 1/x produces a graph with the same vertical and horizontal asymptotes and the same domain and range. In our example, the negative constant not only leaves these unchanged but also “flips” where the branches lie.) Let’s compare: • f(x) = 1/x has:  – vertical asymptote x = 0 and horizontal asymptote y = 0.  – domain: all real numbers except 0.  – range: all real numbers except 0.  – branches in the first and third quadrants. • g(x) = –1/x (obtained by multiplying f by –1) has:  – the same asymptotes (x = 0 and y = 0) since multiplying by –1 does not shift them.  – the same domain and range as f.  – its graph is a reflection across the x-axis; so the branch that was in the first quadrant is now in the second quadrant and the branch that was in the third quadrant is now in the fourth quadrant. Thus, the correct statements are: 1. The graphs have the same asymptotes. 3. The graphs have the same domain and range. 8. The graph of g is in the second and fourth quadrants, while the graph of f is in the first and third quadrants. Therefore, the correct answers are statements 1, 3, and 8.