Question

If you apply the changes below to the absolute value parent function, f(x) =|x|

what is the equation of the new function?
• Shift 5 units right.
• Shift 7 units down,

Answer 1

The new function is g(x) = Ix - 5I - 7 ⇒ answer C

Explanation:

* Lets revise the translation 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

* Now lets solve the problem

∵ f(x) = IxI

∵ f(x) is shifted 5 units to the right

∵ If the function f(x) shifted to the right by h units

∴ g(x) = f(x - h)

- Change IxI to Ix - 5I ⇒ (1)

∵ f(x) is shifted 7 uints down

∵ If the function f(x) shifted down by k units

∴ g(x) = f(x) - k

- Change f(x) to f(x) - 7 ⇒ (2)

- From (1) and (2) the new function is:

g(x) = Ix - 5I - 7

* The new function is g(x) = Ix - 5I - 7