What kind of transformation converts the graph of f(x)=10|x|+4 into the graph of g(x)=2|x|+4?

The transformation that converts the graph of f(x)=10|x|+4 into the graph of g(x)=2|x|+4 is a vertical compression by a factor of 1/5.

Here's the step-by-step explanation:

1. Both functions are in the form of y=a|x|+b, where a is the coefficient of |x| and b is the constant.

2. In the function f(x)=10|x|+4, the coefficient of |x| is 10, and in the function g(x)=2|x|+4, the coefficient of |x| is 2.

3. The change from a coefficient of 10 to a coefficient of 2 represents a vertical compression by a factor of 2/10, or 1/5.

4. Therefore, the transformation from f(x) to g(x) is a vertical compression by a factor of 1/5.

Note: A vertical compression means that the graph is "squeezed" vertically towards the x-axis.