# vertical asymptotes

• Jul 6th 2006, 04:24 PM
Lane
pretest 6 math questions
Find the horizontal asymptote of the graph f(x)= 2/x-4

A: y=2 B: x=0 C: x=4 D: y=0

Find the vertical asymptote(s) if any, for f(x)= 4x-4/x2-5x-6

A: x=-1, x=6, x=4 B: x=-1, x=6 C: x=4, x=-1 D: none

Find the zeros of the function. F(x)= 4x-7/x-2
• Jul 6th 2006, 06:09 PM
ThePerfectHacker
Quote:

Originally Posted by Lane
Find the horizontal asymptote of the graph f(x)= 2/x-4

A: y=2 B: x=0 C: x=4 D: y=0

At this level it is when the denominator is zero. Thus, if you mean $\displaystyle y=\frac{2}{x}-4$ then the answer is $\displaystyle x=0$ and if you mean $\displaystyle y=\frac{2}{x-4}$ then the answer is $\displaystyle x=4$
Quote:

Originally Posted by Lane
Find the vertical asymptote(s) if any, for f(x)= 4x-4/x2-5x-6

A: x=-1, x=6, x=4 B: x=-1, x=6 C: x=4, x=-1 D: none

Factor
$\displaystyle \frac{4(x-1)}{(x+1)(x-6)}$ that happens when $\displaystyle x=-1,6$ (remember set each factor equal to zero).

Quote:

Originally Posted by Lane
Find the zeros of the function. F(x)= 4x-7/x-2

You need an "x" such as,
$\displaystyle \frac{4x-7}{x-2}$ a fraction is only zero when its numerator is zero thus,
$\displaystyle 4x-7=$ thus, $\displaystyle x=7/4=1.75$
• Jul 7th 2006, 06:56 AM
earboth
Quote:

Originally Posted by Lane
Find the horizontal asymptote of the graph f(x)= 2/x-4

A: y=2 B: x=0 C: x=4 D: y=0...

Hello,Lane,

you'll get the horizontal asymptote if calculate the limit of f(x):

a) you mean: $\displaystyle f(x)=\frac{2}{x}-4$. Then $\displaystyle \lim_\csub{|x|\rightarrow\infty} f(x)=-4\ \Longrightarrow\ As: y = -4$

b) you mean: $\displaystyle f(x)=\frac{2}{x-4}$. then $\displaystyle \lim_\csub{|x|\rightarrow\infty} f(x)=0\ \Longrightarrow\ As: y = 0$

The possible answers doesn't include y = -4, therefore the answer is D.

Greetings

EB