Question

Determine the domain and zeros (if any) of the rational function g(x) (x^3-64)/(x^2+5). Also find all intercepts, asymptotes and holes if any

Answer 1

\(\large g(x) = \dfrac{x^3-64}{x^2+5}\)

Answer 2

Are there any "x" values that can make denominator become "0" ?

Answer 3

No

Answer 4

So, No excluded values for this function
that means the Domain the "all real numbers"

Answer 5

I did get that, I'm stuck on the intercepts, asymptotes and holes.

Answer 6

To get the zeroes, set the function equal to 0

Answer 7

For x-intercepts :

\(\large g(x) = \dfrac{x^3-64}{x^2+5} = 0\)


\(\large \implies x^3-64 = 0\)

Answer 8

solve x

Answer 9

X=4 that is my x intercept correct.

Answer 10

Yup !

Answer 11

knw how to find y-intercepts ?

Answer 12

No holes, and my ha would be 3/2 and there would be no va.

Answer 13

Y intercept is 0

Answer 14

Oops ha is x=1

Answer 15

there will not be any ha

Answer 16

No va or ha asymptotes, zero is 4 and intercepts are 4,0

Answer 17

nope

Answer 18

"zeroes" is same as "x-intercepts", so ...
zeroes = 4
x-intercepts = 4

Answer 19

how did u get 0 ?

Answer 20

oh do u mean x-intercept is (4,0) ?

Answer 21

btw, u still need to find y-intercept

Answer 22

Not thinking, if I set x to 0 I would get:
(0-4)(0+ 4(0)+16)
-4(16)=-64
Y=-64?

Answer 23

hmm doesnt look right

Answer 24

To get y-intercepts :

\(\large g(0) = \dfrac{0^3-64}{0^2+5} \)

\(\large g(0) = \dfrac{-64}{5} \)

Answer 25

\(\large\dfrac{-64}{5} \) is ur y-intercept, right ?

Answer 26

Yep. Thank you again. Think I am calling it quits for the day

Answer 27

hold up,
are you taight slant/oblique asymptotes yet ?

Answer 28

if u heard of them before, then u will have to find them as well :)

Answer 29

???

Answer 30

nvm

Answer 31

Ok, have a great Easter!

Answer 32

you too :)