Question

Graph f (x) = x and g (x) = 2/9 x -2. Then describe the transformation from the graph of f (x) = x to the graph of g (x) = 2/9 x -2.

Answer 1

Given:

`f(x)=x\text{ and }g(x)=(2)/(9)x-2`

Required:

We need to find the transformation from f(x) to g(x).

Step-by-step explanation:

Consider the function f(x).

`f(x)=x`

Set x=0 and substitute in the function f(x).

`f(0)=0`

We get the point (0,0).

Set x =9 and substitute in the function f(x).

`f(9)=9`

We get the point (9,9).

Mark the point (0,0) and (9,9) and join them by a ray.

Consider the function g(x).

`g(x)=(2)/(9)x-2`

Set x=0 and substitute in the function g(x).

`g(0)=(2)/(9)(0)-2=-2`

We get the point (0,-2).

Set x=9 and substitute in the function g(x).

`g(9)=(2)/(9)(9)-2=2-2=0`

We get the point (9,0).

Mark the points (0,-2) and (9,0) on the graph and join them by a ray.

The point on f(x) is (9,9)

The point on g(x) is (9,0).

Conisder the function

`f(x)=x`

Multiply x sides by 2/9, it rotates the line f9x)=x.

`f_1(x)=(2)/(9)x`

Subtract 2 from the whole function, it shifts down by 2 units.

`g(x)=(2)/(9)x-2`

Final answer:

The transformation is rotated and translated.