Question
What does the transformation f(x) f(6x) do to the graph of f(x)?
reflects it across the y-axis
reflects it across the x-axis
stretches it horizontally
shrinks it horizontally
reflects it across the y-axis
reflects it across the x-axis
stretches it horizontally
shrinks it horizontally
Answers
GPT-4o mini
The transformation \( f(6x) \) affects the graph of \( f(x) \) by compressing it horizontally.
To break it down:
- The function \( f(6x) \) replaces \( x \) with \( 6x \). This means that for any given value of \( x \), you are now looking at the function's value at \( 6x \), effectively causing the graph to change more rapidly.
- Since you’re multiplying \( x \) by \( 6 \), the effect is to shrink the graph horizontally by a factor of \( 6 \). This means the graph will look "narrower."
So the correct answer is:
**shrinks it horizontally**.
To break it down:
- The function \( f(6x) \) replaces \( x \) with \( 6x \). This means that for any given value of \( x \), you are now looking at the function's value at \( 6x \), effectively causing the graph to change more rapidly.
- Since you’re multiplying \( x \) by \( 6 \), the effect is to shrink the graph horizontally by a factor of \( 6 \). This means the graph will look "narrower."
So the correct answer is:
**shrinks it horizontally**.