Question

Which of the following are the equations for the parent function and the transformed parent function represented by the graph?

Answer 1

Parent function:
`y=(1)/(x)`

Transformed function:
`y=-(1)/(x)`

Explanation:

The given function is a rational function.

The parent rational function is
`f(x)=(1)/(x)`.

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
`g(x)=-(1)/(x)`