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 \( k \) to slowly increase the value of \( k \) from 0 to 3. 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 whatt you observe, conclude if a positive real number \( k \) is added to the output of a function \( y=f(x) \), the graph of the new function \( g(x)=f(x)+k \) is the graph of \( f \) shifted

When you increase the value of \( k \), you will notice that the entire graph of the square root function shifts vertically upwards by \( k \) units. This means that every point on the original \( f(x) = \sqrt{x} \) moves the same distance upward without altering its shape. So, for example, if \( k = 2 \), every point on the graph of \( \sqrt{x} \) will be 2 units higher, making it a simple translation. Now, if you experiment with the other functions in the drop-down menu, you can see how the same principle applies: adding \( k \) consistently shifts the graph upwards regardless of the original function's shape. This intuitive behavior reflects a fundamental property of function transformations, making it easier to visualize how modifications to output affect the overall graph. Grab your imaginary paintbrush and start painting those graphs upward!