Question

Given that f(x) = |x| is the parent of g(x) = |x−2|+1 what transformations have occurred on the graph from f(x) to g(x)? Question 2 options:

Horizontal shift Left 2 and a Vertical shift Up 1.
Horizontal shift Right 2 and a Vertical shift Down 1.
Horizontal shift Right 2 and a Vertical shift Up 1.
Horizontal shift Left 2 and a Vertical shift Down 1.

Answer 1

Horizontal shift Right 2 and a Vertical shift Up 1.

Explanation:

Given that f(x) = |x| is the parent of g(x) = |x−2|+1

g(x)= |x=2|+1

Now we compare it with f(x)

+1 is added at the end

when any number is added at the end then there will be a vertical shift up

when any number is subtracted at the end then there will be a vertical shift down

Here 1 is added at the end , so vertical shift up by 1 unit

If any number added with x , there will be a horizontal shift to the left

If any number subtracted with x , there will be a horizontal shift to the right

In g(x) , 2 is subtracted with x , so horizontal shift 2 units to the right