Reflections About the Origin Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
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Question
Use the image to answer the question.

Four concave curves are drawn on a coordinate plane with the x-axis from negative 6 to 6 and the y-axis from negative 4 to 4, both in increments of 2.

Given the graph of f(x)=x−1−−−−√+1
, which option shows the reflection of the graph about the origin?

(1 point)
The reflection of the graph of f(x)=x−1−−−−−√+1
about the origin is option
.
Remaining Attempts : 3
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Answer 1

To find the reflection of a function \( f(x) \) about the origin, you need to apply the transformation \( f(-x) \) to the function, and then multiply the result by -1.

Given the function:

\[ f(x) = \sqrt{x-1} + 1 \]

1. First, find \( f(-x) \):

\[ f(-x) = \sqrt{-x-1} + 1 \]

2. Next, apply the negative to reflect about the origin:

\[ -f(-x) = -(\sqrt{-x-1} + 1) = -\sqrt{-x-1} - 1 \]

Therefore, the reflection of the graph of \( f(x) \) about the origin would be represented by the new function:

\[ y = -\sqrt{-x-1} - 1 \]

From the choices provided in your assessment, look for an option with this transformed function. If none of the choices are presented here, you would identify it with the appropriate graph shape or features based on the mathematical transformation.