For Algebra 2 Geniuses?

[standfast_lovefirst]

Ok so here is my sob story:I need help with my homework. I am confused and upset. My parents and i have to fly to another state to visit family, which mean i will miss the last week of school. When my math teacher heard about this, he decided to dump the rest of the years assignments on me. I am confused and dont know what to do. Here is what i need to know:The variable z varies jointly with x and y. Use the given values to write an equation relating x y and z. Then find z when x= -4 and y= -71. x= -6 y= -3 z= 2/52. x= 3/8 y= 16/17 z= 3/2Write an equation for the given relationship1. y varies jointly with z and the sqaure root of xIdentify the horizontal and vertical asymptotes of the graph of the function. Then state domain and range.1. y=4/x-3+22. y=x=2/x-33.y=-3x+2/-4x-54.y=34x-2/16x+4

[Yankees135]

1) so what you are trying to do is get an equation for z in terms of x and y.This means the equation will look something like z = ax + by where you need to figure out what a and b are.You have 2 different values. You know that when z = 2/5, x= -6, and y = -3.so you have2/5 = -6a -3bYou can get a similar equation from the second point (z = 3/8, y=16/17, z = 3/2)Then you have a pair of equations which I'm guessing you've seen how to solve two variable, two equations ?(Once you have z = whatever, you can find z when x=-4 and y = -7 by plugging in x and y into the equations)2)An asymptote occurs on a graph when something gets really really close to a line, but doesn't quite reach it.For example, if you have the equation y = 1/x . When x gets really big, 1 / x gets really close to 0. But it never quite reaches zero since 1 divided by a big number is still a little more than zero. This is called a horizontal asymptote because if you draw the graph of y = 1/x, the graph will almost look like a line.A vertical asymptote occurs when the graph gets either really really big or really really small. Again, if you think of y = 1/x, think about when x gets really really small ( like .000000001 ) The function 1/x gets really really big. This causes a vertical asymptote.The way you find horizontal asymptotes is normally by thinking about what happens to y as x gets really really big or really really negative. So in number 1, when x gets really big, on the positive side. y = 4 / (a really big number -3 ) + 2 "a really big number - 3" is still a really big number. So 4 / a really big number is basically going to be zero. Then when you add 2 to it, you get 2. So there is a horizontal assymptote at y = 2, because when x gets really large y gets really close to 2, but never touches it. Then think of what happens when x gets really negative. In this case it is 4 / a really negative number, which is still about zero, so the same thing happens.Sometimes these can be more complicated like in 4.When x gets really large what happens to(34x - 2) / (16x + 4).Well the thing to remember is that when x is that big, adding or subtracting 2 or 4 won't make much difference compared with multiplying by 34 (think about the difference between 100 * 34 and 100 + 2. When you multiply the change is much much more). It turns out in this case that the 34 and the 16 are much more important. So the horizontal asymptote occurs at y = 34/16For vertical assymptote, they occur wherever a denominator is zero normally. So in the case of number 1, the denominator is zero whenever x-3 is zero , meaning when x = 3. Domain is wherever the function is defined. Normally, a function is defined for all values of x. But, a function is not defined whenever a denominator is zero. So the domain will be all real numbers except [blank] , where blank is wherever the denominator is zero. For number 1 for example, it would be all real numbers except for x = 3, because that is where the denominator is zero.For range, it is what possible values y can take. This is often all real numbers, but sometimes you can conclude that y is always bigger than something or y is always smaller than something.Hope this helps some. Sorry that it is a bit long-winded