The given question asks for the equation of the new function when certain transformations are applied to the absolute value parent function $F(x) = |x|$.

Transformations:

1. Horizontal compression by a factor of 11:

   • A horizontal compression is applied by multiplying the input $x$ by 11. This affects the equation inside the absolute value brackets. So, $F(x) = |x|$ becomes $F(x) = |11x|$.

2. Shift upward by 4 units:

   • This transformation adds 4 to the output of the function, shifting the graph upward by 4 units. So the new equation becomes $F(x) = |11x| + 4$.

Conclusion:

The correct equation is $G(x) = |11x| + 4$, which corresponds to option A.

Would you like further details or have any questions? Here are some related questions for practice:

1. How does a horizontal stretch differ from a horizontal compression?
2. What happens if you shift the function $F(x) = |x|$ downward instead of upward?
3. How would you describe a vertical stretch of the function $F(x) = |x|$?
4. What is the general form of a transformed absolute value function?
5. If the function were shifted to the left or right, how would the equation change?

Tip: Remember that horizontal transformations affect the input $x$, and vertical transformations affect the output of the function.