Question

If you apply the changes below to the absolute value parent function, f(x) = [X,which of these is the equation of the new function?• Shift 2 units to the left.• Shift 3 units down.O A. g(x) = 5x + 21 - 3O B. g(x) = (x - 21 - 3O c. g(x) = 5x + 31 - 2O D. g(x) = \x - 31 - 2

Answer 1

`\begin{gathered} f(x)=\lvert x\rvert \\ \\ g(x)=\lvert x-h\rvert+k \\ \\ _{} \end{gathered}`

h is the translation left or right

h > 0 the function shifts to the right h units

h < 0 the function shifts to the left h units

k is the translation up or down

k > 0 the function shifts up k units

k < 0 the function shifts down k units

For the given transformations:

Shift 2 units to the left. h: -3

Shift 3 units down. k: -3

Then, the function g(x) is:

`\begin{gathered} g(x)=\lvert x-(-2)\rvert-3 \\ \\ g(x)=\lvert x+2\rvert-3 \end{gathered}`