Question

How to find the intercepts and asymptotes of f(x)=2x^2+x-2/x^2-1

Answer 1

Is the function\[f(x)=\frac{ 2x^2+x-2 }{ x^2-1}\]

Answer 2

yes

Answer 3

OK lets start with intercepts. What is the interception with y-axis? Isnt it when x=0?

Answer 4

sorry, intercept with y-axis

Answer 5

yeah

Answer 6

so, what is the value of f(x) when x=0?

Answer 7

f(0)=2(0)^2+0-2/(0)^2-1=-2/-1=2

Answer 8

Perfect! Now The x-axis crossing! Arent they the values of x that make y=0? And arent the values that make y=0 the same values that make the numerator=0?

Answer 9

so I have to get the numerator equal to zero

Answer 10

Bingo!

Answer 11

so 0=2x^2+0-2, how can I solve that

Answer 12

i meant +x not +0

Answer 13

You have to solve:\[2x^2+x-2=0\]the formula to solve an equation like:\[ax^2+bx+c=0\rightarrow x=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\]I dont believe you didnt know this formula

Answer 14

in your case a=2, b=1 and c=-2, find the two solutions

Answer 15

I get:x1=0.78 and x2=-1.28 do you ge the same?

Answer 16

you there?

Answer 17

yeah how did you get the .78 and 1.28 when you get left off with \[-1\pm \sqrt{5}\div4\]

Answer 18

so, for you b^2-4ac = 5?

Answer 19

a=2 b=1 c=-2-->b^2-4ac=1-4·2·(-2)=1+16=17

Answer 20

oops i found my mistake , ok I'm with you now

Answer 21

so its \[-1\pm \sqrt{17}\div4\]

Answer 22

Those are the cross points for x-axis

Answer 23

Now find the roots of the denominator. It is straightforward

Answer 24

how do you do that

Answer 25

what are the values of x that make the denomnator =0?

Answer 26

I am sorry, I have to go. To be continued tomorrow, bye

Answer 27

i've figured it out and the asymptotes. can you help me find the x-intercept of x^2-2x+3/x+2