Fill in the blank(s) to correctly complete each sentence.
The graph of ƒ(x) = √-x is a reflection of the graph of y = √x across the ___-axis.

Verified step by step guidance

1. Identify the basic function: The function \( y = \sqrt{x} \) is a standard square root function.
2. Understand the transformation: The function \( f(x) = \sqrt{-x} \) involves a transformation of \( y = \sqrt{x} \).
3. Recognize the effect of the negative sign: The negative sign inside the square root, \( \sqrt{-x} \), indicates a reflection.
4. Determine the axis of reflection: A negative sign inside the function \( \sqrt{-x} \) reflects the graph across the y-axis.
5. Complete the sentence: The graph of \( f(x) = \sqrt{-x} \) is a reflection of the graph of \( y = \sqrt{x} \) across the y-axis.

Key Concepts

Reflection in Graphs

Reflection in graphs refers to the flipping of a graph over a specific axis. For instance, reflecting a graph across the x-axis means that for every point (x, y) on the original graph, there is a corresponding point (x, -y) on the reflected graph. This concept is crucial for understanding how transformations affect the shape and position of functions.

Square Root Function

The square root function, denoted as y = √x, is defined for non-negative values of x and produces non-negative outputs. Its graph is a curve that starts at the origin (0,0) and increases gradually. Understanding the properties of this function helps in analyzing its transformations, such as reflections and shifts.

Transformation of Functions

Transformation of functions involves changing the position or shape of a graph through operations like translations, reflections, and stretches. In this case, reflecting the square root function across the x-axis alters its output values, leading to the function ƒ(x) = √-x, which is defined for non-positive x values. Recognizing these transformations is essential for manipulating and interpreting function graphs.