Rational Fuctions - I need help with Step 5 and 6.

[robthebear]

I need help with Step 5 and 6.

Step 5 - I do not know how to get the Hole part of the answer. I looked in the book but do not see it in there. I got the x = -3 part. But can someone show me how to get the Hole part. My teacher did not go over that part.

Step 6 – The book says that there is no HA intersect but when I put.
(x^2 - 3x - 10) / (x^2 + 8x + 15) = 1 I get x = 25/11 am I doing something wrong here?

Here is my work: (x^2 - 3x - 10) / (x^2 + 8x + 15) = 1
(x^2 - 3x - 10) = (x^2 + 8x + 15)
- 3x - 10 = 8x + 15
11x = 25
x = 25/11 or 2.27



28. R (x)= (x^2 - 3x - 10) / (x^2 + 8x + 15)

On problem 28 follow steps 1 through 9.

Step 1: Find the domain of the rational function.
Step 2: Write R in Lowest terms.
Step 3: Locate the intercepts of the graph. The x-intercepts, if any, of R (x) = p(x) / q(x) in lowest terms satisfy the equation p(x) = 0. The y-intercepts, if there is one, is R (0).
Step 4: Test for symmetry.
Step 5: Locate the vertical asymptotes.
Step 6: Locate the horizontal or oblique asymptotes, if any.
Step 7: List the zeros of the numerator and the zeros of the denominator of R. Create a table to locate points on the graph around each of these zeros.
Step 8: Graph R using a graphing utility.
Step 9: Use the results to obtained in Step 1 through 8 to graph R by hand.

Answers:
1. Domain {x l x cannot = -3, x cannot = -5}
2. R(x) = (x – 2) / (x + 3)
3. x-intercept = 2, y-intercept = -2/3
4. No Symmetry.
5. Vertical Asymptote: x = -3, Hole at (-5, 3.5)
6. Horizontal asymptote: y = 1, not intersected
7. Table x l y1
-8 l 2
-4 l 6
0 l -.6667
8 l .54545
8. Graph…
9. Graph…

 

[Denis]

Here is my work: (x^2 - 3x - 10) / (x^2 + 8x + 15) = 1
(x^2 - 3x - 10) = (x^2 + 8x + 15)
- 3x - 10 = 8x + 15
11x = 25
x = 25/11 or 2.27

11x = -25 (you musta been looking at some of Unco's work!)

 

[wjm11]

Robthebear,

Please check your factoring and simplifying in part 2, paying special attention to signs.

Check your intercepts again. Using the original form of the eqn, set x=0 to find the y intercept. Set the numerator =0 to find x intercepts.

I agree with Denis regarding the HA intersect. I recommend you graph this to examine function behavior. It's always nice to have a picture.

If your book says there is no HA intersect, it could be an error in the book, or you may have copied the problem down wrong. Please check.

Hope this helps.