Question
What does the transformation f(x)-f(x) do to the graph of f(x)?
stretches it horizontally
reflects it across the y-axis
reflects it across the x-axis
shrinks it horizontally
stretches it horizontally
reflects it across the y-axis
reflects it across the x-axis
shrinks it horizontally
Answers
GPT-4o mini
The transformation \( f(x) - f(x) \) simplifies to \( 0 \). This means that for every value of \( x \), the function returns a constant value of zero.
### Effect on the Graph:
- The graph of \( f(x) - f(x) \) translates to a horizontal line at \( y = 0 \).
### Conclusion:
This transformation does not fit the options provided like stretching, reflecting, or shrinking. Instead, it effectively collapses the entire function into a horizontal line at \( y = 0 \). The most accurate description is that it results in a graph where all values of \( f(x) \) are subtracted from themselves, resulting in the constant function \( f(x) - f(x) = 0 \).
### Effect on the Graph:
- The graph of \( f(x) - f(x) \) translates to a horizontal line at \( y = 0 \).
### Conclusion:
This transformation does not fit the options provided like stretching, reflecting, or shrinking. Instead, it effectively collapses the entire function into a horizontal line at \( y = 0 \). The most accurate description is that it results in a graph where all values of \( f(x) \) are subtracted from themselves, resulting in the constant function \( f(x) - f(x) = 0 \).