To answer each part, I’ll outline what is generally involved in determining these characteristics from a graph. If you can upload the graph image, I can provide a detailed, precise response based on the specific function shown. Here’s a general approach:

Steps to Solve:

1. Domain and Range:

   • Domain is the set of all $x$-values for which the function is defined. On a graph, it is determined by the leftmost and rightmost points of the curve, as well as any gaps or vertical asymptotes.
   • Range is the set of all $y$-values the function attains. It is determined by the lowest and highest points the graph reaches and any horizontal asymptotes.

2. Intercepts:

   • $x$-intercepts occur where the function crosses the $x$-axis (i.e., where $y = 0$).
   • $y$-intercepts occur where the function crosses the $y$-axis (i.e., where $x = 0$).

3. Horizontal Asymptotes:

   • Look for any horizontal lines the graph approaches as $x \to \infty$ or $x \to -\infty$.

4. Vertical Asymptotes:

   • Look for any vertical lines the graph approaches but never crosses. Vertical asymptotes typically occur where the function is undefined due to division by zero.

5. Oblique Asymptotes:

   • If the function does not have a horizontal asymptote and instead approaches a slanted line as $x \to \infty$ or $x \to -\infty$, it may have an oblique asymptote.

Please upload the image for a detailed analysis.

Would you like to continue with any additional details on these concepts or have specific questions?

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Related Questions:

1. How do you determine the asymptotes of a rational function?
2. What are the conditions for a function to have an oblique asymptote?
3. How does the domain change if there are vertical asymptotes?
4. How are intercepts affected by transformations of the function?
5. Can a function have both a horizontal and an oblique asymptote?

Tip: For rational functions, vertical asymptotes often occur where the denominator is zero (if those points do not cancel with the numerator).