College Algebra
posted by Kameesha .
Using the 7 steps outlined in section 4.3 of your book, analyze the graph of the following function:
R(x) = x^2  49/x^4  16
Step 1: Factor the numerator and denominator of R and find its domain. If 0 is in the domain, find yintercept, R(0), and plot it.
Step 2: Write R in lowest terms as p(x)/q(x) and find the real zeros of the numerator; that is, fnd the real solutions of the equation p(x) = 0, if any. These are the xintercepts of the graph. Determine the behavior of the graph of R near each xintercept, using the same procedure as for polynomial functions. Plot each xintercept and indicate the behavior of the graph near it.
Step 3: With R written in lowest terms as p(x)/q(x), find the real zeros of the denominator; that is, find the real solutions of the equation q(x) = 0, if any. These determine the vertical asymptotes of the graph. Graph each vertical asymptote using a dashed line.
Step 4: : Locate any horizontal or oblique asymptotes using the procedure given in the previous section. Graph the asymptotes using a dashed line. Determine the points, if any, at which the graph of R intercepts these asymptotes. Plot any such points.
Step 5: Using the real zeros of the numerator and the denominator of the given equation for R, divide the xaxis into intervals and determine where the graph is above the xaxis and where it is below the xaxis by choosing a number in each interval and evaluating R there. Plot the points found.
Step 6: Analyze the behavior of the graph of R near each asymptote and indicate this behavior on the graph.
Step 7: Put all the information together to obtain the graph of R.

I suggest look at the 7 steps in the text. I certainly have no idea what they are.

Evidently the accompanying essay describes the steps.
1. (x7)(x+7) / (x2)(x+2)(x^2+4)
2. zeros: x=7,7
3. vert asymp: x = 2,2
4. degree of top < degree of bottom: hor. asymp at y=0
57: visit
wolframalpha . com
or
rechneronline . de/functiongraphs/ 
R(x)=x^3125/x^249