Graph (dy)/(dx)=-x/y


Step 1
Find where the expression is undefined.

Step 2
The vertical asymptotes occur at areas of infinite discontinuity.
No Vertical Asymptotes

Step 3
Consider the rational function where is the degree of the numerator and is the degree of the denominator.
1. If , then the x-axis, , is the horizontal asymptote.
2. If , then the horizontal asymptote is the line .
3. If , then there is no horizontal asymptote (there is an oblique asymptote).

Step 4
Find and .

Step 5
Since , there is no horizontal asymptote.
No Horizontal Asymptotes

Step 6
Find the oblique asymptote using polynomial division.

Move the negative in front of the fraction.
Negate .
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
-+
Divide the highest order term in the dividend by the highest order term in divisor .
-
-+
Multiply the new quotient term by the divisor.
-
-+
-
The expression needs to be subtracted from the dividend, so change all the signs in
-
-+
+
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
-
-+
+
Pull the next terms from the original dividend down into the current dividend.
-
-+
+
+
Divide the highest order term in the dividend by the highest order term in divisor .
-+
-+
+
+
Multiply the new quotient term by the divisor.
-+
-+
+
+
+
The expression needs to be subtracted from the dividend, so change all the signs in
-+
-+
+
+
-
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
-+
-+
+
+
-
Since the remander is , the final answer is the quotient.
The oblique asymptote is the polynomial portion of the long division result.

Step 7
This is the set of all asymptotes.
No Vertical Asymptotes
No Horizontal Asymptotes
Oblique Asymptotes:

Step 8


Related Questions