Question

What is the value of h in the translation of the given function?  Describe the phase shift (use a phrase like 3 units to the left). g(x) = f(x +6)

Answer 1

It is a translation along the x-axis by 6 units to the left

Answer 2

Answer:

The value of h = 6  and the phase shift is 6 units to the left.

Step-by-step explanation:

Definition: For a parent function y =f(x),

the transformation y=f(x+h) is a shift of the function either right or left.

If h < 0 ; then the shift is a right shift by h units

If h > 0 ;  then the shift is a left shift by h units.

Given the function:

$g(x) = f(x+6)$

by definition;

h = 6 > 0

⇒in the given function, the shift is 6 units to the left.

Therefore, the value of h = 6  and the phase shift is 6 units to the left.