use the graph shown to find the following (a) the domain and range of the function (b) the intercepts, if…

Explanation:

Step1: Identify domain from graph

The graph has a vertical asymptote at (x = 0). The function is not defined at (x=0). So the domain is all real - numbers except (x = 0), written as ({x|x\neq0}).

Step2: Identify range from graph

The graph has a horizontal asymptote at (y = 0). The function approaches (y = 0) but never reaches it. So the range is all real - numbers except (y = 0), written as ({y|y\neq0}).

Step3: Find x - intercepts

The graph does not cross the (x) - axis, so there are no (x) - intercepts.

Step4: Find y - intercepts

The graph does not cross the (y) - axis, so there are no (y) - intercepts.

Step5: Find horizontal asymptote

As (x\to\pm\infty), the function approaches (y = 0). So the horizontal asymptote is (y = 0).

Step6: Find vertical asymptote

The function is undefined at (x = 0) and the graph approaches infinity as (x\to0). So the vertical asymptote is (x = 0).

Step7: Find oblique asymptote

Since the degree of the numerator is less than the degree of the denominator (assuming a rational - function form), there is no oblique asymptote.

Answer:

(a) Domain: A. The domain of the function is ({x|x\neq0}) Range: A. The range of the function is ({y|y\neq0}) (b) Intercepts: No (x) - intercepts and no (y) - intercepts (c) Horizontal asymptote: (y = 0) (d) Vertical asymptote: (x = 0) (e) Oblique asymptote: None