Given the parent function f(x)=1x, what transformations were applied to create the function g(x)=1x−7−10?
two downward shifts.
To determine the transformations applied to the parent function f(x)=1x to create the function g(x)=1x−7−10, we need to analyze the changes in the equation.
The general form of the parent function f(x)=1x is y=1x. This function does not have any transformations applied to it. It represents a straight line passing through the origin, with a slope of 1.
In the function g(x)=1x−7−10, there are two transformations applied:
1. Vertical Translation: The term "-7" in the equation represents a vertical translation of 7 units downwards. This means the graph of g(x) has been shifted 7 units below the original function f(x)=1x.
2. Vertical Translation: Similarly, the term "-10" in the equation represents a vertical translation of 10 units downwards. This additional term shifts the graph of g(x) an additional 10 units below the transformed function.
To summarize:
- The term "-7" represents a vertical translation of 7 units downwards.
- The term "-10" represents a vertical translation of 10 units downwards.
Using these transformations, the function g(x) is obtained from the parent function f(x).