equation of asymptotes

[Louise Johnson]

I need find the equations of asymptotes for the following functions:

1) f(x) = 4 / (x^2 + 1)

2) g(x) + -8/(x - 4) I think this one is x=4 y=0

3) i(x) = square root of 10 - x - 2

 

[stapel]

I need find the equations of asymptotes for the following functions:

Your book and/or class gave you formulas and rules for this process. How far have you gotten in applying those?

1) f(x) = 4 / (x^2 + 1)

This is a rational function, with a very simple rule to apply. Check your book.

2) g(x) + -8/(x - 4) I think this one is x=4 y=0

Since we don't know what g(x) is, there seems little way to determine what the asymptotes might be. Since you have, there must be additional information which was not included. Please reply with that, along with a clarification of what you mean by the "plus minus" in the middle of the expression above.

3) i(x) = square root of 10 - x - 2

Your formatting is ambiguous. Do you mean any of the following?

. . . . .i(x) = sqrt[10] - x - 2

. . . . .i(x) = sqrt[10 - x] - 2

. . . . .i(x) = sqrt[10 - x - 2]

. . . . .i(x) = sqrt[10 - x]^(-2)

Or something else?

Thank you.

Eliz.

 

[Louise Johnson]

#1
f(x) = 4 / (x^2 + 1)
After graphing this one I came up with a Domain of "R"
Range (0,4]
x intercept none
y intercept 4
Asymptotes confused if there is none or if y= 0 or i should just state none because y=0 ?

#2
g(x) = -8/(x - 4) I think this one is x=4 y=0 Sorry that was my error having a plus sign instead of the equal symbol

#3
i(x) = sqrt[10 - x - 2] This was the correct formatting. Thank you This one I think there is none as the graph will continue to grow infinetly

 

[stapel]

#1 After graphing this one I came up with a Domain of "R" Range (0,4] x intercept none y intercept 4

The domain and range are correct, as are the intercepts.

Asymptotes confused if there is none or if y= 0 or i should just state none because y=0 ?

Since zero exists, "y = 0" and "no asymptote exists" cannot be the same. You'll need to pick one.

#2 I think this one is x=4 y=0 Sorry that was my error having a plus sign instead of the equal symbol
Are these asymptotes, intercepts, or something else?

[quote="Louise Johnson":1mi3fxi5]#3 This was the correct formatting.

[/quote:1mi3fxi5]
A good first start might be to simplify the very odd formatting. Since 10 - 2 = 8, then sqrt[10 - x - 2] = sqrt[8 - x].

Eliz.

 

[Louise Johnson]

Since zero exists, "y = 0" and "no asymptote exists" cannot be the same. You'll need to pick one.

I am going with the asymptote y=0 for the graph of f(x)=4/x^2+1

#2 I think this one is x=4 y=0 Sorry that was my error having a plus sign instead of the equal symbol

Are these asymptotes, intercepts, or something else?

Yes they are my answers for asymptotes for the function g(x) = -8/(x - 4)

i(x) = sqrt[10 - x - 2] or sqrt[8 - x] (thank you)

Domain of (-infinty,8]
Range [0,infinity)
x intercept 8
y intercept 2 sqrt 2
no asymptotes

Thank you for your replies!