Question

What type of transformation takes the graph of f(x)=|x| to the graph of g(x)=|4+x|?

vertical translation of 4 units up
horizontal translation of 4 units left
horizontal translation of 4 units right
vertical translation of 4 units down

Answer 1

translation to the left by 4 units

Answer 2

horizontal translation of 4 units left

Explanation:

the graph of f(x)=|x| to the graph of g(x)=|4+x|

In g(x) , 4 is added with x

The rule of transformation is

f(x) -> f(x-a), horizontal translation of 'a' units right

f(x) -> f(x+a), horizontal translation of 'a' units left

f(x) -> f(x)+a, Vertical translation of 'a' units up

f(x) -> f(x)-a, Vertical translation of 'a' units down

When we compare f(x) and g(x), 4 is added with x

f(x) -> f(x+a), horizontal translation of 'a' units left

So its a horizontal translation of 4 units left