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

Explanation:

Step1: Determine the domain

The domain is the set of all x - values for which the function is defined. Looking at the graph, the function is defined for all real x - values except x = 0. So the domain is $(-\infty,0)\cup(0,\infty)$.

Step2: Determine the range

The range is the set of all y - values that the function takes. From the graph, the function takes all real y - values except y = 0. So the range is $(-\infty,0)\cup(0,\infty)$.

Step3: Find the intercepts

To find the x - intercept, we set y = 0. From the graph, the function never crosses the x - axis, so there is no x - intercept. To find the y - intercept, we set x = 0, but the function is not defined at x = 0, so there is no y - intercept.

Step4: Find horizontal asymptotes

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

Step5: Find vertical asymptotes

The function is not defined at x = 0 and as $x\to0^{+}$ and $x\to0^{-}$, the function goes to $\pm\infty$. So the vertical asymptote is x = 0.

Step6: Find oblique asymptotes

Since the degree of the numerator is less than the degree of the denominator (assuming the function is a rational function based on the shape of the graph), there are no oblique asymptotes.

Answer:

(a) Domain: $(-\infty,0)\cup(0,\infty)$ (b) Intercepts: None (c) Horizontal asymptote: y = 0 (d) Vertical asymptote: x = 0 (e) Oblique asymptote: None