What does the transformation 

f

(

x

)

↦

f

(

6

x

)

 do to the graph of 

f

(

x

)

?

The transformation \( f(x) \mapsto f(6x) \) compresses the graph of the function horizontally by a factor of \( \frac{1}{6} \).

Here's why:
- The transformation \( f(kx) \) generally affects the graph of \( f(x) \) horizontally.
- If \( k > 1 \), the graph of \( f(x) \) is compressed horizontally by a factor of \( \frac{1}{k} \).
- In this case, \( k = 6 \), so the graph is compressed by a factor of \( \frac{1}{6} \).

Thus, all x-values are scaled down by 6, meaning points on the graph will appear closer to the y-axis compared to the original function.

Would you like more details or have any questions?

### Related Questions:
1. What happens if we apply \( f(x) \mapsto f\left(\frac{x}{6}\right) \)?
2. How does the transformation \( f(x) \mapsto f(-x) \) affect the graph?
3. What does the transformation \( f(x) \mapsto 6f(x) \) do to the graph of \( f(x) \)?
4. Can you describe the effect of \( f(x) \mapsto f(x - 6) \) on the graph?
5. What happens to the graph under the transformation \( f(x) \mapsto -f(x) \)?

**Tip:** Horizontal transformations occur inside the function argument, affecting the x-values of the graph, while vertical transformations act outside, affecting the y-values.

What does the transformation f(x) ↦ f(6x) do to the graph of f(x)?

Discover how the transformation f(x) ↦ f(6x) affects the graph of f(x). This transformation compresses the graph horizontally by a factor of 1/6, bringing points closer to the y-axis. Learn the math behind function transformations, suitable for Grades 10-12 students.

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