To describe the transformation of the function [tex]\( y=\sqrt{x} \)[/tex] to [tex]\( y=\sqrt{x+4} \)[/tex], let's break it down step-by-step.
1. Identify the Parent Function:
- The parent function here is [tex]\( y = \sqrt{x} \)[/tex].
2. Understand the Inside-Function Transformation:
- The transformation involves modifying the argument inside the square root. In this case, the argument [tex]\( x \)[/tex] is transformed to [tex]\( x + 4 \)[/tex].
3. Determine the Transformation:
- When you add a constant inside the square root (or inside any function of [tex]\( x \)[/tex]), it translates the graph horizontally. The focus is on how [tex]\( x \)[/tex] is modified.
- For [tex]\( y = \sqrt{x+4} \)[/tex], compare it to [tex]\( y = \sqrt{x} \)[/tex]. The expression [tex]\( x+4 \)[/tex] means that for any [tex]\( x \)[/tex] value of the parent graph, you need to use [tex]\( x - 4 \)[/tex] for the new function to obtain the same [tex]\( y \)[/tex] value.
- Therefore, the modification [tex]\( x \)[/tex] becomes [tex]\( x-4 \)[/tex] in the horizontal direction. But since inside the function it's written as [tex]\( x+4 \)[/tex], it suggests the [tex]\( x \)[/tex]-values in the parent function will shift to the left by 4 units (because substituting [tex]\( x \)[/tex] with [tex]\( -4 \)[/tex] makes it a zero inside the function).
Thus, the transformation that describes the shift from [tex]\( y = \sqrt{x} \)[/tex] to [tex]\( y = \sqrt{x+4} \)[/tex] is a shift left 4 units.
So the correct transformation is:
- Shift left 4 units
