Question
What does the transformation f(x) f(4x) do to the graph of f(x)?
stretches it horizontally
stretches it vertically
shrinks it horizontally
shrinks it vertically
stretches it horizontally
stretches it vertically
shrinks it horizontally
shrinks it vertically
Answers
GPT-4o mini
The transformation \( f(4x) \) affects the graph of \( f(x) \) by shrinking it horizontally.
To understand why, we can consider how the input \( x \) is being modified. The \( 4x \) means that for any given value of \( y \) on the graph of \( f(x) \), it will occur at \( x/4 \) on the graph of \( f(4x) \). Essentially, you have to reach a smaller \( x \) value to get the same \( y \) output, which compresses the graph towards the y-axis.
Thus, the correct answer is:
**shrinks it horizontally**.
To understand why, we can consider how the input \( x \) is being modified. The \( 4x \) means that for any given value of \( y \) on the graph of \( f(x) \), it will occur at \( x/4 \) on the graph of \( f(4x) \). Essentially, you have to reach a smaller \( x \) value to get the same \( y \) output, which compresses the graph towards the y-axis.
Thus, the correct answer is:
**shrinks it horizontally**.