Question: Consider the function f ( x ) = 2 x ^ 2 + 5 x - 3 / 5 x ^ 2 + 1 9

Consider the function f(x)=2x^2+5x-3/5x^2+19x+12. Answer the questions and follow the directions below. 1. What is the domain of the function? Show all steps in your process. 2. Determine whether each domain restriction results in a vertical asymptote or a hole, and explain how you know. 3. What is the end behavior of the function? Show all steps in your process. 4. Determine whether the function crosses the asymptote you found in Question 3. Show all steps in your process. 5. What are the intercepts (x or y) of the function? Show all steps in your process. 6. Add the information you calculated in Questions 1-5 to your graph, but don't fill in the actual graph yet. 7. For what values of x could the function possibly change from positive to negative, or vice versa? 8. Use your answers in Question 7 to divide the real numbers up into interesting intervals, and make a sign chart for the function. 9. Use the information from your sign chart in Question 8 to complete your sketch of the graph of the function. 10. Use the graph to determine the range of the function.

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