To apply a horizontal shrink by a factor of 1/3 to the function $f(x) = |x - 1| + 3$, we need to adjust the $x$-variable in a specific way.

Horizontal Shrink:

A horizontal shrink by a factor of $\frac{1}{3}$ means that every $x$-coordinate in the graph of the function is scaled by a factor of 3. This is equivalent to replacing $x$ with $3x$ in the function.

Applying the transformation:

1. Start with the original function: $f(x) = |x - 1| + 3$

2. Apply the horizontal shrink by replacing $x$ with $3x$: $f(3x) = |3x - 1| + 3$

Final result:

The new function after the horizontal shrink is: $f(x) = |3x - 1| + 3$

This is the function resulting from applying the horizontal shrink by a factor of $\frac{1}{3}$ to the original function $f(x) = |x - 1| + 3$.

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Would you like a more detailed explanation of horizontal transformations, or have any other questions on this?

Here are some related questions to explore further:

1. How do vertical and horizontal shifts affect the graph of a function?
2. What would happen if we applied a horizontal stretch instead of a shrink?
3. How can we transform other absolute value functions?
4. What is the difference between a horizontal and a vertical transformation?
5. How would the horizontal shrink impact the slope of the graph?

Tip: Horizontal transformations (shrinks or stretches) affect the $x$-coordinate directly by replacing $x$ with a scaled version, such as $3x$ for a horizontal shrink.