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

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10