To understand how the parent function [tex]\( f(x) = \frac{1}{x} \)[/tex] is transformed to create the function [tex]\( f(x) = \frac{200}{x} + 10 \)[/tex], let's analyze each transformation step by step.
1. Vertical Stretch by a Factor of 200:
- The original function is [tex]\( f(x) = \frac{1}{x} \)[/tex].
- When we multiply the function by 200, we get [tex]\( f(x) = \frac{200}{x} \)[/tex].
- This transformation stretches the function vertically by a factor of 200.
2. Vertical Shift Up by 10 Units:
- After the vertical stretch, we have the function [tex]\( f(x) = \frac{200}{x} \)[/tex].
- Adding 10 to this function shifts it vertically upward by 10 units.
- Therefore, the new function becomes [tex]\( f(x) = \frac{200}{x} + 10 \)[/tex].
Combining these transformations:
- First, the function [tex]\( f(x) = \frac{1}{x} \)[/tex] is vertically stretched by a factor of 200.
- Then, the function [tex]\( f(x) = \frac{200}{x} \)[/tex] is shifted 10 units up.
The correct description of the transformations is:
It is vertically stretched by a factor of 200 and shifted 10 units up.
