Question

HELP PLEASE!!
F(x)=x+(50/x^3)

a)What is the domain of F(x)? Chose one answer
1. x does not equal to o and +-^4squareroot of 50
2. x does not equal 0 and ^4squareroot of 50
3. x does not equal 0
4. All real numbers

b)What is the equation of the vertical asymptote(s) of F(x)?
1. x=__________ (use comma to separate answer as needed. Type an integer or a fraction)
OR
2. there is no vertical asymptote

c)What is the equation of the horizontal of oblique asymptote of F(x)?
1. y=________
OR
2. there is no horizontal or oblique

Answer 1

domain-
find a value of x when f(x) has either
1. a division by 0 or
2. square-root of -ve number

Domain is then all number except for those you just found.

Answer 2

confused still?

Answer 3

\[f(x)=x+{50\over x^3}\]
when can you get a division by 0 here?

Answer 4

no

Answer 5

what if x=0?

Answer 6

but you can't divide by 0

Answer 7

exactly...
so, you cannot have x=0 in the domain of f(x)

Answer 8

domain is any 'x' for which you can calculate f(x)

Answer 9

okay what about +- \[\sqrt[4]{50}\]

Answer 10

it is still a number.
1. does it give you a division by 0?
2. does it give you a sqre-root of -ve number?
NO
so, \[\sqrt[4]{50}\] is a valid number.

Answer 11

ooooh! okay

Answer 12

but if you had \[\sqrt[4]{-50}\], you cannot have that. so, that x=-50 would not be in the domain

Answer 13

what would the vertical asymptote be then?

Answer 14

vertical asymptote - the value of 'x' that the function approaches but never really gets there

Answer 15

now, you can have 0.0000000000001 and -0.00000000001 but not 0
so, you can approach x=0 but not get there

Answer 16

so, vertical asymptote -> x=0

Answer 17

okay so meaning that they horzontal/oblique asymptote is x?

Answer 18

no.. asymptote of f(x)...
I just explained vertical.. similarly for hortizontal.. value of y but never gets there

Answer 19

so, we say that y "will" get there only at infinity... so, replace x by 1/u simplify, and put u=0.
the value of f(x) you get will be your horizontal asymptote

Answer 20

oblique is that f(x) comes close to some line but never intercepts it.

Answer 21

well I graph the equation that isn't it a oblique asymptote?

Answer 22

no there are no oblique asymptotes here