which function has the following characteristics? vertical asymptote at x=3. and horizontal asymptote at y=2. Domain {x =with a cross through it plus minus 3}

Question

which function has the following  characteristics? vertical asymptote at x=3. and horizontal asymptote at y=2. Domain {x =with a cross through it plus minus 3}

smored · Answer

$$x \neq \pm3$$
that?

anonymous · Answer

yeah

smored · Answer

tkhunny shall answer

anonymous · Answer

do I need to put anything else?

tkhunny · Answer

You should put the answer choices, perhaps?   :-)

Start with a bare function and build it a step at a time.

$y = \dfrac{}{}$

vertical asymptote at x=3

$y = \dfrac{}{x-3}$

horizontal asymptote at y=2

$y = \dfrac{2x}{x-3}$

Domain {x =with a cross through it plus minus 3}

This hint is a little tricky.  There is a vertical asymptote at x = 3, so x = 3 is not in the Domain.  What's the deal with x = -3?

If there is a vertical asymptote at x = -3, there are two necessary adjustments.

$y = \dfrac{2x^{2}}{(x-3)(x+3)}$

If there is a NOT vertical asymptote at x = -3, it's just missing, there are two necessary adjustments.

$y = \dfrac{2x(x+3)}{(x-3)(x+3)}$

This is NOT a unique function.  There are many fitting these few criteria.  Perhaps one of them on your list is close?

anonymous · Answer

a. y=2x-8/x-3 b. y=2x^2 -8/x^2-9 c. y=2x^2-18/x^2-4 d. y=x^2-9/x^2-4

tkhunny · Answer

a) x = -3 is IN the Domain.  No good.
b) Pretty good.  This is very close to what I have, excepting the "-8".  This is it!!
c) Both x = 2 and x = -2 are NOT in the Domain, but x = 3 and x = -3 are.  No good.
d) Horizontal asymptote is the x-axis.  No good.