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/
Answer this Question
Related Questions
college algebra--need help please!! - (Using the seven steps to analyzing the ...
college algebra - analyze the graph of the following function. r(x)= x^2+x-6...
college algebra !!! - analyze the graph of the following function. r(x)= x^2+x-6...
college algebra - Graph the following function using transformations. ...
college algebra - Question 638522: Graph the following function using ...
college algebra - graph the following function using transformations, be sure to...
College Algebra - Graph the following function using transformations. Be sure to...
College alg - Analyze the graph of the following function as follows: (a) Find ...
College Algebra - 1.Answer the following for the given quadratic function. f(x...
college algebra - graph the following function using transformations, be sure to...
For Further Reading
