1. Finding holes in a function! Help please!

Can you please find the hole(s) in these three functions?

f(x) = x^2-x-6 / 2x^2 -x- 6

f(x) = -x^3-7x^2-12x / 3x^2-11x-20

f(x) = x^2+4x-5 / x^4-4x^3+3x^2

Thanks so much! If you can't do one don't worry about it! All the work helps!

2. Hello, Sbach2010!

Find the hole(s) in these three functions.

. . $f(x) \:= \:\frac{x^2-x-6}{2x^2 -x- 6}$

Factor: . $f(x) \;=\;\frac{(x+2)(x-3)}{(x-2)(2x+3)}$

It has vertical asymptotes at: . $x \,=\,2\text{ and }x \,=\,-\tfrac{3}{2}$
. . but no holes

$f(x) \:= \:\frac{-x^3-7x^2-12x}{3x^2-11x-20}$

Factor: . $f(x)\;=\;\frac{-x(x+3)(x+4)}{(x-5)(3x+4)}$

It has vertical asymptotes at: . $x\,=\,5\text{ and }x\,=\,-\tfrac{4}{3}$
. . but no holes.

$f(x) \:= \:\frac{x^2+4x-5}{x^4-4x^3+3x^2}$

Factor: . $f(x)\;=\;\frac{(x-1)(x+5)}{x^2(x-1)(x-3)}$

It has vertical asymptotes at: . $x \,=\,0\text{ and }x\,=\,3$

. . and a hole at (1, -3).

3. Thank you that was very helpful!

Now what are the x and y intercepts for each funtion?

Also the Domain of each?

Help much appreciated!

4. To find the y-intecept, you need to set x = 0 for the equation
To find the x-intecept, you need to set y = 0 for the equation
To find the domain of the function, you can refer to this useful link for guidance 2a. Domain and Range of a Function

Hope it helps.

Originally Posted by Sbach2010
Thank you that was very helpful!

Now what are the x and y intercepts for each funtion?

Also the Domain of each?

Help much appreciated!