graph the function ( y = x^{2}-2x - 8 ) by identifying the domain and any symmetries, finding the…

graph the function ( y = x^{2}-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. \nc. the function has no horizontal asymptotes. \nfind any oblique asymptotes. select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. \na. the function has one oblique asymptote, (type an equation.) \nb. the function has two oblique asymptotes. the asymptote with smaller slope is and the asymptote with larger slope is (type equations.) \nc. the function has no oblique asymptotes.

graph the function ( y = x^{2}-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. \nc. the function has no horizontal asymptotes. \nfind any oblique asymptotes. select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. \na. the function has one oblique asymptote, (type an equation.) \nb. the function has two oblique asymptotes. the asymptote with smaller slope is and the asymptote with larger slope is (type equations.) \nc. the function has no oblique asymptotes.

Answer

Explanation:

Step1: Recall the definition of oblique asymptote

An oblique asymptote occurs for a rational function (y = \frac{f(x)}{g(x)}) when the degree of (f(x)) is one more than the degree of (g(x)). For a polynomial function (y = ax^{n}+bx^{n - 1}+\cdots+z) ((n\geq2)), there are no oblique asymptotes.

Step2: Analyze the given function

The function (y=x^{2}-2x - 8) is a polynomial function of degree (n = 2). Since it is not a rational function (in the form (\frac{f(x)}{g(x)}) with (g(x)\neq1)) and for polynomial functions of degree (n\geq2), there are no oblique asymptotes.

Answer:

C. The function has no oblique asymptotes.