If f(x) = |x| and g(x) = |x| - 4, which transformation is applied to f(x) to get g(x)?

Solution:

Given: Functions are f(x) = |x| and g(x) = |x| - 4

We have the general formula of transformations as f(x) = a(bx - h)ⁿ + k

Here, k is the vertical shift, h is the horizontal shift, a is the vertical stretch, and b is the horizontal stretch.

On comparing g(x), we get k = -4

From the graph we can observe that we are shifting 4 down

Therefore, the transformation applied is translation and is down by 4.

If f(x) = |x| and g(x) = |x| - 4, which transformation is applied to f(x) to get g(x)?

Summary:

If f(x) = |x| and g(x) = |x| - 4, the transformation applied to f(x) to get g(x) is translation and is down by 4.