Answer:
Parent function: [tex]y=\frac{1}{x}[/tex]
Transformed function: [tex]y=-\frac{1}{x}[/tex]
Step-by-step explanation:
The given function is a rational function.
The parent rational function is [tex]f(x)=\frac{1}{x}[/tex].
This is a hyperbola that is found in the first and third quadrant that is asymptotic to the axes.
The transformed function is a a hyperbola that is asymptotic to the axes and it is located in the second and fourth quadrant.
The point (1,1) on the parent function corresponds to (-1,1) on the transformed function.
The point (-1,-1) on the parent function corresponds to (1,-1) on the transformed function.
We can observe that the x-coordinates were negated in each case.
This the rule for a reflection in the y-axis.
Therefore the transformed function has equation [tex]g(x)=-\frac{1}{x}[/tex]
