1. ## HELP Isotope questions

What are the asymptotes of the graph of y= 3 + 5 ?
2x-6

What are the asymptotes of the graph of y = 2 -7 ?
x+18

The variable z varies directly with y and inversely with x. When x-4 and y = 28, z = 56. Which equation relates to x, y, and z?

z = 8y
X
z= xy
56

z= 8xy
z= 56xy

Is there anyone that can help me??? PLEASE a mom that has long since forgotten this stuff trying to help daughter!!!

2. Originally Posted by chessmaster
What are the asymptotes of the graph of y= 3 + 5 ?
2x-6

What are the asymptotes of the graph of y = 2 -7 ?
x+18

The variable z varies directly with y and inversely with x. When x-4 and y = 28, z = 56. Which equation relates to x, y, and z?

z = 8y
X
z= xy
56

z= 8xy
z= 56xy

Is there anyone that can help me??? PLEASE a mom that has long since forgotten this stuff trying to help daughter!!!
If I'm reading what you have written correctly, you would like to find the asymptotes of $\displaystyle y = \frac{3}{2x-6} + 5$ and $\displaystyle y = \frac{2}{x + 18} - 7$. An asymptote is simply a function that the graph approaches for increasing or decreasing values of x. And in these cases, the important factor is that x is in the denominator. When you have x in the denominator, the constant part of the denominator becomes less important for increasing values of x. So for the first question, the asymptote is $\displaystyle y = \frac{3}{2x} + 5$ and for the second question, the asymptote is $\displaystyle y = \frac{2}{x} - 7$. The correct answer to your proportionality question is $\displaystyle z = \frac{8y}{x}$. This is because when two variables a and b are directly proportional, they are related by $\displaystyle a = kb$ for some constant k, and when a and b are inversely proportional, they are related by $\displaystyle a = \frac{k}{b}$ or $\displaystyle ab = k$ for some constant k.

3. Originally Posted by icemanfan
If I'm reading what you have written correctly, you would like to find the asymptotes of $\displaystyle y = \frac{3}{2x-6} + 5$ and $\displaystyle y = \frac{2}{x + 18} - 7$. An asymptote is simply a function that the graph approaches for increasing or decreasing values of x.

Mr F says: You are referring to a particular type of asymptote known as an oblique asymptote. Horizontal asymptotes are a special case of such asymptotes.

There is another type of asymptote known as a vertical asymptote. These asymptotes are vertical lines passing through values of x that make the function undefined.

And in these cases, the important factor is that x is in the denominator. When you have x in the denominator, the constant part of the denominator becomes less important for increasing values of x. So for the first question, the asymptote is $\displaystyle y = \frac{3}{2x} + 5$ and for the second question, the asymptote is $\displaystyle y = \frac{2}{x} - 7$.

Mr F says: NO! This is wrong.

[snip]
$\displaystyle y = \frac{3}{2x-6} + 5$:

Vertical asymptote found by solving 2x - 6 = 0: x = 3.

Horizontal asymptote found by considering the limits x --> oo and x --> -oo: $\displaystyle y \rightarrow 0 + 5 = 5$.

--------------------------------------------------------------------------

$\displaystyle y = \frac{2}{x + 18} - 7$.

Vertical asymptote found by solving x + 18 = 0: x = -18.

Horizontal asymptote found by considering the limits x --> oo and x --> -oo: $\displaystyle y \rightarrow 0 - 7 = -7$.

4. Originally Posted by chessmaster
[snip]
The variable z varies directly with y and inversely with x. When x-4 and y = 28, z = 56. Which equation relates to x, y, and z?

z = 8y
X
z= xy
56

z= 8xy
z= 56xy

Is there anyone that can help me??? PLEASE a mom that has long since forgotten this stuff trying to help daughter!!!
$\displaystyle z = \frac{k y}{x}$.

Substitute the given data: $\displaystyle 56 = \frac{28 k}{4} = 7k \Rightarrow k = 8$.

Therefore $\displaystyle z = \frac{8 y}{x}$.