Use the graph shown to find the following a The domain and r

Use the graph shown to find the following. (a) The domain and range of the function (b) The intercepts, if any (c) Horizontal asymptotes, if any (d) Vertical asymptotes, if any (e) Oblique asymptotes, if any (a) What is the domain? Select the correct choice below and fill in any answer boxes within your choice. A. The domain of the function is {x| }. (Type an inequality. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain of the function in the graph is the set of all real numbers. What is the range? Select the correct choice below and fill in any answer boxes within your choice. A. The range of the function is {y| }. (Type an inequality Use integers or fraction for any numbers in the expression. Use a comma to separate answers as needed.) B. The range of the function in the graph is the set of all numbers. (b) Find the x-intercepts, if there are any, Select the correct choice below and fill in any answer bores with your choice. A. x =

Solution

From the graph, we see that

(a) The graph is defined for all x, except at x=4, therefore the domain = R - {4}.

(b) The graph passes through a single point i.e. origin, therefore both x and y intercepts are zero.

(c) The horizontal asymptote is at y = -4,

(d) The vertical asymptote is at x = 4, and

(e) There exists no oblique asymptote.