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.

검증된 단계별 안내

Identify the original function and the transformed function. The original function is \(y = \sqrt{x}\), and the transformed function is \(f(x) = -\sqrt{x}\).

Recognize that the negative sign in front of the square root affects the output values (the \(y\)-values) of the function, changing their sign.

Understand that changing the sign of the \(y\)-values corresponds to reflecting the graph across the \(x\)-axis.

Therefore, the graph of \(f(x) = -\sqrt{x}\) is a reflection of the graph of \(y = \sqrt{x}\) across the \(x\)-axis.

Fill in the blank with '\(x\)' to complete the sentence: 'The graph of \(f(x) = -\sqrt{x}\) is a reflection of the graph of \(y = \sqrt{x}\) across the \(x\)-axis.'

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Square Root Function

The square root function, y = √x, produces the principal (non-negative) root of x and is defined for x ≥ 0. Its graph starts at the origin and increases slowly, forming a curve in the first quadrant. Understanding this base function is essential before analyzing transformations.

Reflection Across an Axis

Reflection across an axis means flipping a graph over that axis, creating a mirror image. Reflecting a function y = f(x) across the x-axis changes it to y = -f(x), inverting all y-values. This concept helps identify how the graph of y = -√x relates to y = √x.

Function Transformations

Function transformations include shifts, stretches, compressions, and reflections that alter a graph's position or shape. Recognizing how multiplying a function by -1 reflects it across the x-axis is key to completing the sentence about the graph of ƒ(x) = -√x.

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.