Given:
[tex]f(x)=x\text{ and }g(x)=\frac{2}{9}x-2[/tex]
Required:
We need to find the transformation from f(x) to g(x).
Explanation:
Consider the function f(x).
[tex]f(x)=x[/tex]
Set x=0 and substitute in the function f(x).
[tex]f(0)=0[/tex]
We get the point (0,0).
Set x =9 and substitute in the function f(x).
[tex]f(9)=9[/tex]
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).
[tex]g(x)=\frac{2}{9}x-2[/tex]
Set x=0 and substitute in the function g(x).
[tex]g(0)=\frac{2}{9}(0)-2=-2[/tex]
We get the point (0,-2).
Set x=9 and substitute in the function g(x).
[tex]g(9)=\frac{2}{9}(9)-2=2-2=0[/tex]
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
[tex]f(x)=x[/tex]
Multiply x sides by 2/9, it rotates the line f9x)=x.
[tex]f_1(x)=\frac{2}{9}x[/tex]
Subtract 2 from the whole function, it shifts down by 2 units.
[tex]g(x)=\frac{2}{9}x-2[/tex]
Final answer:
The transformation is rotated and translated.
