Question

graph w\
graph x\
graph y\
graph z\
complete this statement given th\\(\quad\\)\\( = -f(x)\\).\
the graph of function \\(g\\) is graph \
\\(\quad\\) because the graph of function \\(g\\) is the result of a \\(\quad\\) applied to\
function \\(f\\).

Explanation:

Step1: Identify base function graph

First, assume Graph X is the parent function \(f(x)\) (a positive reciprocal function in the first quadrant, \(f(x)=\frac{k}{x}, k>0, x>0\)).

Step2: Analyze transformation \(g(x)=-f(x)\)

The transformation \(g(x)=-f(x)\) reflects the graph of \(f(x)\) across the x-axis. This means all y-values of \(f(x)\) are multiplied by -1, so positive y-values become negative, and the graph moves to the fourth quadrant for positive x-values.

Step3: Match transformed graph

Graph Y is the reflection of Graph X across the x-axis, matching \(g(x)=-f(x)\).

Answer:

The graph of function \(g\) is graph Y because the graph of function \(g\) is the result of a reflection across the x-axis applied to function \(f\).