Question

Can someone teach me some things about inverse variation?

Answer 1

@jim_thompson5910

Answer 2

what things come to mind when you think of the word "inverse" ?

Answer 3

opposite

Answer 4

i know that direct variation can be calculated by \(y = kx\) and inverse variation can be calculated by \(yx = k\)

Answer 5

is that correct?

Answer 6

you are correct on all 3 statements

Answer 7

inverse variation is where as x goes up, y goes down, or vice versa. We "opposite" movements here

in terms of algebra, multiplying x and y will give you a fixed number every time

x*y = k

and you can solve for y to get y = k/x

Answer 8

can you give me a problem with inverse variation?

Answer 9

Let's say you had a rectangle and you knew the area was 120

the sides of the rectangle are unknown, but you know that there are 2 pieces of unknown info, the other 2 sides are equal to the first two unknowns

so we have x and y unknown and this rectangle has area 120

so

area = length*width
120 = x*y
x*y = 120

as you can see, this fits the form x*y = k where k is the constant and k = 120 in this case

Answer 10

one possible combo of x,y is

x = 30
y = 4

x*y = 120
30*4 = 120
120 = 120

now let's say that x were to increase to 60. What happens to y? it would go down to y = 2. X goes up, y goes down

Answer 11

and asymptote can be calculated when the denominator equals to 0 right. so if the denominator was x - 2, then the asymptote would be 2.

Answer 12

`and asymptote can be calculated when the denominator equals to 0 right. so if the denominator was x - 2, then the asymptote would be 2.`

correct

Answer 13

okay thanks :)

Answer 14

well you'd say x = 2 but you get the idea

Answer 15

anything else that i need to know?

Answer 16

how about the horizontal asymptote?

Answer 17

"and asymptote can be calculated when the denominator equals to 0 right. so if the denominator was x - 2, then the asymptote would be 2." More precisely, if the denominator of a rational expression happens to be zero at some x value or values, that tells you right then and there the equation(s) of the vertical asymptote(s).

Answer 18

So: if the denom. were x-2, the vert. asy. would be x=2. Need to label that 2.

Answer 19

i don't know about the horizontal asymptote

Answer 20

Well, let's try this:

Supposing you have inverse variation: y=k/x.

What happens to y as x continues to increase in magnitude?

Answer 21

y decreases

Answer 22

Horiz. asy. have to do with the behavior of a rational function when x grows large, either in the positive or the neg direction.

Yes, and decreases toward what value in particular?

Answer 23

What if x=10, x=100, x=1000, etc.?

Answer 24

i don't know by what you meant when saying `decreases toward what value in particular`

Answer 25

What if x=-10, x=-100, x=-1000, etc?

What behavior do you see in y? Does y seem to have a limiting value?

Answer 26

when x increases, y decreases

Answer 27

Actually, it was "when the function y decreases toward what value in particular?"

Answer 28

Or, more generally, what happens to the value of y as x continues to increase in either the + or the - direction?

This all has to do with limits. Hope I'm not getting too far ahead of where you are in y our present class.

Answer 29

we did not learn limits unfortunately