2. for f(x) = 2(x+3) - 5, name the type of function and describe each of the
three transformations from the parent function f(x) = x

The function is a linear function

The function is translated 3 units to the left,then stretched vertically

by factor 2, then translated 5 units down

Step-by-step explanation:

* Lets revise some transformation

- 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

- If the function f(x) stretched vertically, then g(x) = k · f(x), where

 k > 1 (multiplying each of its y-coordinates by k)

- If the function f(x) compressed vertically, then g(x) = k · f(x), where

 0 < k < 1 (multiplying each of its y-coordinates by k)

* Now lets solve the problem

∵ f(x) = 2(x + 3) - 5

- The greatest power of the function is 1 (degree of the function)

∴ f(x) is linear function

- The parent function f(x) = x

∵ f(x) changed to f(x + 3)

∴ f(x) translated 3 units to the left

# Each x-coordinate of the points on the function subtracted by 3

∵ f(x + 3) changed to 2f(x + 3)

∵ 2 > 1

∴ f(x + 3) stretched vertically by factor 2 (k = 2)

# Each y-coordinate of the points on the function multiplied by 2

∵ 2f(x + 3) changed to 2f(x + 3) - 5

∴ 2f(x + 3) translated 5 units down

# Each y-coordinate of the points on the function subtracted by 5

the weight of the object inside the box!