Yis directly related to x , and y is 81 when x is 27.

the constant of variation is

 3

Step-by-step explanation:

When a variable is directly varies to variable y , then the equation for direct  variation is given by :_

                               (1)

, where k is the constant of variation.

We are given that ,

Y is directly related to X , and Y is 81 when X is 27.

Put x= 27 and y= 81 in (1) , we get

Divide both sides by 27  , we get

  or

That is , the constant of variation = 3

step-by-step explanation:

if you meant, "on the way from (3, 2) to (3, 14):

x does not change; y increases by 12.

ensure that you have copied down this problem correctly.   .

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: