Question

F

Answer 1

"f(x) = the quantity two x squared plus one divided by the quantity x squared minus four"

lol no.

Answer 2

horizontal is 2

Answer 3

Use parentheses next time. is it f(x)= (2x^2+1)/(x^2-4)
Time to learn how to use the equation editor, though...\[\large f(x)= \frac{2x^2+1}{x^2-4}\]

Answer 4

sorry

Answer 5

I know there is one 2 but I think there is another too correct?

Answer 6

Vertical asymptotes: find what x-values make the denominator equal to zero.

Horizontal asymptotes: compare highest exponent terms on top and bottom - since they're the same, you just divide the coefficients

Answer 7

Explain clearly what you are doing.

Answer 8

vertical values blow up to infinity and the function doesnt exist at those values, figure out the values if any

horizontal values - look at the limit for huge x values, limit as x goes off to +/-infinity

Answer 9

i don't want to explain i don't have time; i did my work so thats good enough i told you i got two 2's

Answer 10

can you help

Answer 11

@JoCelM

Answer 12

someone pleasee!

Answer 13

vertical asmytopes - where f(x) doesnt exist, it is a fraction, if the bottom is zero, it is undefined, so when x^2 - 4 = 0, the function will not exist, x=+2 and x=-2

Answer 14

notice as you get closer to those values x=+2 and x=-2 , the denominator gets smaller and smaller, and so the function will get larger and larger

Answer 15

Horizontal values - look at the limits at infinty, if there is a value

\[\large \lim_{x \rightarrow \infty} \frac{2x^2+1}{x^2-4}\]

Answer 16

doing a bit of algebra, you can divide everything by the highest power x^2 to get

\[\large \lim_{x \rightarrow \infty} \frac{(2x^2+1)/x^2}{(x^2-4)/x^2}=\large \lim_{x \rightarrow \infty} \frac{2+\frac{ 1 }{ x^2 }}{1-\frac{ 4 }{ x^2 }}\]

notice the fractions 1/x^2 and 4/x^2 will go to zero as x goes to infinity, so the limit is
2/1 , same thing if you put in -infinty, you get limit 2

Answer 17

graph the thing and check if it looks good

Answer 18

"i don't want to explain i don't have time; i did my work so thats good enough"

Then i don't have time to help you. And no, I expect you to show your work, just like any math teacher will.