Question

what is the effect of the transformation $y = \sqrt{x} + 4$ compared to $y = \sqrt{x}$?
shift right by 4 units
shift up by 4 units
shift left by 4 units
shift down by 4 units

Explanation:

Step1: Recall Vertical Shift Rule

For a function \( y = f(x) + k \), if \( k>0 \), the graph shifts up by \( k \) units; if \( k<0 \), it shifts down.
Here, \( f(x)=\sqrt{x} \), and the transformed function is \( y = \sqrt{x}+4 \), so \( k = 4>0 \).

Step2: Determine Transformation

Applying the vertical shift rule, adding 4 to the function \( y=\sqrt{x} \) (i.e., \( y = \sqrt{x}+4 \)) shifts the graph of \( y=\sqrt{x} \) up by 4 units.

Answer:

B. Shift up by 4 units