Question

Describe the transformation that occurred on f(x) to create g(x).

Tranlslated:
A. 6 units to the right
B. 6 units to the left
C. 7 units to the right
D. 7 units to the left

and:

A: 6 units up
B. 6 units down
C. 7 units up
D. 7 units down

Reflection:
A. Did occur
B. Did not occur
C. Can't be determined

Answer 1

f(x) translated 3 units to the left and 8 units down, there is no reflection occurred

Explanation:

* Lets revise some transformation for the functions

- If the function f(x) reflected across the x-axis, then the new

function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

function g(x) = f(-x)

- 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

* Now lets study the problem

∵ g(x) = 2(x + 3)² - 8

# x + 3 ⇒ means f(x) translated 3 units to the left

# -8 ⇒ means f(x) translated 8 units down

# There is no reflection occurred