Question
What does the transformation f(x)↦
1/5
f(x) do to the graph of f(x)?
stretches it horizontally
shrinks it vertically
shrinks it horizontally
stretches it vertically
1/5
f(x) do to the graph of f(x)?
stretches it horizontally
shrinks it vertically
shrinks it horizontally
stretches it vertically
Answers
GPT-4o mini
The transformation \( f(x) \mapsto \frac{1}{5} f(x) \) affects the graph of \( f(x) \) by shrinking it vertically.
Here's why:
- The transformation involves multiplying the output of the function \( f(x) \) by \( \frac{1}{5} \).
- This means that for any input \( x \), the output (or \( y \)-value) will be one-fifth of what it was in the original function \( f(x) \).
- As a result, all points on the graph will be lower, leading to a vertical compression of the graph by a factor of 5.
Therefore, the correct answer is that it **shrinks it vertically**.
Here's why:
- The transformation involves multiplying the output of the function \( f(x) \) by \( \frac{1}{5} \).
- This means that for any input \( x \), the output (or \( y \)-value) will be one-fifth of what it was in the original function \( f(x) \).
- As a result, all points on the graph will be lower, leading to a vertical compression of the graph by a factor of 5.
Therefore, the correct answer is that it **shrinks it vertically**.