Given the function f(x) = g(x-3)-2, describe transformation of f(x) on a coordinate plane relative to g(x).

f(x) is obtained by translate g(x) 3 units to the right and 2 units down

Step-by-step explanation:

* Lets talk about the transformation of a function

- If the function f(x) translated horizontally to the right  

by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

by k units, then the new function g(x) = f(x) – k

* Lets study the problem and solve it

∵ f(x) = g(x - 3) - 2

- x-coordinate change from x to x - 3, that means

# x-coordinate is translated 3 units to the right

- y-coordinate change from y to y - 2, that means

# y-coordinate is translated 2 units down

∴ The transformation is:

  translated 3 units to the right and 2 units down

* f(x) is obtained by translate g(x) 3 units to the right and 2 units down

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

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