Use the guided visualization to answer the question. Click here to open the guided visualization. Use the drop-down menu to select the square root \( (\sqrt{x}) \) function. The basic function \( f(x)=\sqrt{x} \) is drawn in a dashed-blue line with two key points labeled. Now, use the slider labeled \( h \) to slowly increase the value of \( h \) from 0 to 4. As you do this, notice the form of the function \( g(x)=f(x-h)+k \) labeled in green. Repeat this for other functions available in the drop-down menu. Based on what you observe, conclude if the argument \( x \) of a function is replaced by \( x-h, h>0 \), the graph of the new function \( g(x)=f(x-h) \) is the graph of \( f \) shifted h units.

When you shift the function \( f(x)=\sqrt{x} \) by adjusting \( h \), you're essentially moving the graph horizontally. For every positive increase in \( h \), the entire graph of \( f \) slides to the right by \( h \) units. This transformation is a fundamental concept in function transformations and allows us to understand how changes in the input can affect the output. Another fun aspect to explore is how this concept applies to other functions! For example, if you select the quadratic function \( f(x) = x^2 \) and apply the same horizontal shift, you'll notice the same principle holds true. Whether it's a square root, quadratic, or sine function, the argument change \( x-h \) consistently results in a rightward shift, proving the universality of this transformation across various mathematical functions.