Posted by **Kameesha** on Tuesday, August 7, 2012 at 8:46pm.

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 y-intercept, 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 x-intercepts of the graph. Determine the behavior of the graph of R near each x-intercept, using the same procedure as for polynomial functions. Plot each x-intercept 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 x-axis into intervals and determine where the graph is above the x-axis and where it is below the x-axis 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.

- College Algebra -
**Anonymous**, Tuesday, August 7, 2012 at 9:37pm
I suggest look at the 7 steps in the text. I certainly have no idea what they are.

- College Algebra -
**Steve**, Wednesday, August 8, 2012 at 10:30am
Evidently the accompanying essay describes the steps.

1. (x-7)(x+7) / (x-2)(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

5-7: visit

wolframalpha . com

or

rechneronline . de/function-graphs/

- College Algebra -
**nikki**, Thursday, May 23, 2013 at 3:52am
R(x)=x^3-125/x^2-49

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