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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

1 answer

To find the reflection of a function \( f(x) \) about the origin, we need to find the expression for \( f(-x) \). This transformation involves replacing \( x \) with \( -x \) in the original function.

Given the function: \[ f(x) = \sqrt{x - 1} + 1 \]

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

This means that the reflection of the graph about the origin will be represented by the new function \( g(x) = f(-x) \).

Summary:

  1. The original function is \( f(x) = \sqrt{x - 1} + 1 \).
  2. The reflection of the graph about the origin is given by \( g(x) = \sqrt{-x - 1} + 1 \).

Selection of Option:

Since I cannot see the image you are referring to, I cannot directly choose one of the options for you. However, look for the graph that represents the equation \( g(x) = \sqrt{-x - 1} + 1 \), which should show a reflection of the original function across the origin, matching the transformation we performed.