A little help with identifying asymptotes. ?

Question

Can someone please help me.

I'm supposed to identify the asymptotes for each function.

1. y = 6/x

2. y = 4/x - 3

3. y = 5/x - 1

5. y = 3/x + 4

I have no clue how to identify the asymptotes.

But, I'm also suppposed to graph it, so if anyone could please tell me how to graph it??

((are asymptotes just points to graph.))

Answer 1

vertical and horizontal asymptote for each

1) x= 0 ,y =0

2) x = 3, y=0

3) x = 1, y=0

4) x = -4 , y=0

really easy way to indentify vertical asymptotes

just set the value to the denominator to zero and solve for x

and this x-value is where the graph cannot have a particular value or its value is infinite

for horizontal asymptotes if the degree of the polynomial in the denominator is GREATER than the degree of the polynomial in numerator then the only asymptote is y = 0

now if the degrees are equal, then the horizontal asymptotes is EQUAL to a/b where a is the LEADING coefficient of numerator polynomial where terms are arranged in descending order and b is the LEADING coefficient of denominator polynomial where terms are arranged in descending order

and if denominator polynomial degree is LESS than numerator polynomial degree then there are NO horizontal asymptotes

asymptotes are imaginary lines which graph can't touch or intersect and they help you to graph function but they are not points

hope this helps

Answer 2

Ok. There are sometimes places were some graphs just don't want to go. Sometimes these areas are just points. Sometimes they're lines. When the exclusions are lines, the lines are called asymptotes.

Most of the time asymptotes can be identified by finding the values where the denominator (bottom number) of a rational expression (like a fraction) gets to be zero.

How about y = (5/x) + 5?

You know that x can never = 0.

What happens to (5/x) + 5 when x is close to zero?

Well, when x = -10, y= 3

When x = -5, y = 4

When x = -1 y = 4.8

When x = -1/5, y = 30

When x = -1/500, y = 2505.

So, when x gets close to zero from the negative side, y gets very large positively... But, since x can never get TO zero, It appears x=0 is what is called an asymptote.

You can do the same thing from the positive side, and you'll find similar results.

How about y = 5/(x+5)?

This is different. Now x can easily become zero. But it can't become -5 because now x+5 can never be allowed to become zero. So the line x=-5 becomes the asymptote.

See how it works?

Answer 3

Asymptotes are lines where the graphs can't touch.

1. y = 6/x

x cannot be 0, so the asymptotes are at x=0, and y=0

2. y = 4/x - 3

x cannot be 0, so the asymptotes are at x=0, and y=-3

3. y = 5/x - 1

x cannot be 0, so the asymptotes are at x=0, and y=-1

5. y = 3/x + 4

x cannot be 0, so the asymptotes are at x=0, and y=4