graph the function y = x² - 2x - 8 by identifying the domain and any symmetries, finding the derivatives y…

graph the function y = x² - 2x - 8 by identifying the domain and any symmetries, finding the derivatives y and y, finding the critical points and identifying the functions behavior at each one, finding where the curve is increasing and where it is decreasing, finding the points of inflection, determining the concavity of the curve, identifying any asymptotes, and plotting any key points such as intercepts, critical points, and inflection points. then find coordinates of absolute extreme points, if any. find any oblique asymptotes. select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. a. the function has one oblique asymptote, (type an equation.) b. the function has two oblique asymptotes. the asymptote with smaller slope is and the asymptote with larger slope is (type equations.) c. the function has no oblique asymptotes. graph the function y = x² - 2x - 8. choose the correct graph below.

graph the function y = x² - 2x - 8 by identifying the domain and any symmetries, finding the derivatives y and y, finding the critical points and identifying the functions behavior at each one, finding where the curve is increasing and where it is decreasing, finding the points of inflection, determining the concavity of the curve, identifying any asymptotes, and plotting any key points such as intercepts, critical points, and inflection points. then find coordinates of absolute extreme points, if any. find any oblique asymptotes. select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. a. the function has one oblique asymptote, (type an equation.) b. the function has two oblique asymptotes. the asymptote with smaller slope is and the asymptote with larger slope is (type equations.) c. the function has no oblique asymptotes. graph the function y = x² - 2x - 8. choose the correct graph below.

Answer

Explanation:

Step1: Recall the definition of oblique asymptotes

An oblique asymptote occurs for a rational - function of the form $y=\frac{f(x)}{g(x)}$ where the degree of $f(x)$ is one more than the degree of $g(x)$. The given function $y = x^{2}-2x - 8$ is a polynomial function of degree 2. Polynomial functions of degree 2 or higher do not have oblique asymptotes.

Step2: Conclusion

Since $y=x^{2}-2x - 8$ is a polynomial function of degree 2, it has no oblique asymptotes.

Answer:

C. The function has no oblique asymptotes.