did I do this right ?

[mattflint50]

I was given the equation (x+2) (x-5)(3x-2)/(x-5) (x+5) (x+1) and I was told to find the zeros, verticle and horizontal asymptotes, and disconinuities.

To find the Zeros I set the numerator equal to 0: And ended up getting x=-2 and x=2/3

To find the horizontal asymptotes is took the ratio of the leading coefficients and got y=3

to find the veritcle asymptotes I set the denomentor equal to zero and got x=-5 and y=-1

I also found one discontinuity at x=5

Did I do this right? Please help.

 

[soroban]

Hello, mattflint50!

I was given the equation \(\displaystyle f(x)\:=\:\frac{(x\,+\,2)(x\,-\,5)(3x\,-\,2)}{(x\,-\,5)(x\,+\,5)(x\,+\,1)\)
and I was told to find the zeros, vertical and horizontal asymptotes, and discontinuities.

To find the Zeros I set the numerator equal to 0.
And ended up getting \(\displaystyle x = -2\) and \(\displaystyle x = \frac{2}{3}\;\) Yes!
You didn't mention x = 5 . . . good point!

To find the horizontal asymptotes, I took the ratio of the leading coefficients and got \(\displaystyle y = 3\;\) Right!

To find the veritcal asymptotes, I set the denomentor equal to zero and got \(\displaystyle x=-5\) and \(\displaystyle x = -1\;\) Correct!

I also found one discontinuity at \(\displaystyle x=5\;\) Great work!

 

[mattflint50]

thank you very much