Which relationship shows an inverse variation? x: 2,3,4,5 f(x): 1,4,9,16 x: 1,2,3,4 f(x): 2,8,18,32 x: 1,2,3,4 f(x): 4,3,2,1 x: 2,4,6,8 f(x): 12,6,4,3,

x  :  2,4,6,8

f(x) :12,6,4,3

This table represents the relationship of an inverse variation.

Step-by-step explanation:

We are asked to find which relationship shows an inverse variation.

Inverse variation means that there exist a constant 'k' such that:

f(x)=k/x

or, k=x·f(x)

1)

x  :   2, 3, 4, 5

f(x):  1,  4, 9, 16

if x=2 and f(x)=1

k=2

but if x=3 and f(x)=4

we get: k=12.

Hence, we do not obtain a same constant k.

2)

x:   1,2,3,4

f(x):2,8,18,32

when x=1 , f(x)=2

⇒ k=2

when x=2 , f(x)=8

⇒ k=16

Hence, we did not get a same constant 'k'.

3)

x:  1,2,3,4

f(x):4,3,2,1

when x=1, f(x)=4

⇒ k=4

when x=2 , f(x)=3

⇒ k=6

Hence, we did not get a same constant 'k'.

4)

x  :2,4,6,8

f(x) :12,6,4,3

when x=2 f(x)=12

⇒ k=2×12=24

when x=4  f(x)=6

⇒ k=4×6=24

when x=6    f(x)=4

⇒   k=6×4=24

when x=8   f(x)=3

⇒  k=8×3=24

Hence, we get a constant 'k=24' for all the values of x.

Hence, option: 4 shows relationship of an inverse variation.

x  :2,4,6,8

f(x) :12,6,4,3

4.08%

step-by-step explanation:

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)