Use the graphs of  $f$f​  and $h$h​  to describe the transformation from the graph of  $f$f​  to the graph of $h$h​ .

$f\left(x\right)=-2x-2$f(x)=−2x−2​

$h\left(x\right)=f\left(5x\right)$h(x)=f(5x)​

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The graph of $h$h​  is a Response area of the graph of  $f$f​  by a factor of Response area.

The transformation from the graph of $ f(x) = -2x - 2 $ to the graph of $ h(x) = f(5x) $ involves a **horizontal compression**.

To answer the questions specifically:

- The graph of $ h $ is a **horizontal compression** of the graph of $ f $.
- The factor of compression is by a factor of **$ \frac{1}{5} $**.

This means that each point on $ h(x) $ is horizontally compressed to be closer to the y-axis by a factor of 5 compared to the corresponding point on $ f(x) $. 

Let me know if you need more explanation or have questions about these transformations!

Here are some follow-up questions:
1. What effect does multiplying $ x $ by a factor greater than 1 have on a graph horizontally?
2. How would $ h(x) = f(\frac{x}{2}) $ compare in transformation to $ f(x) $?
3. What does a negative coefficient in $ f(x) = -2x - 2 $ imply about the graph’s orientation?
4. How would adding a constant inside $ h(x) = f(5x) + 3 $ affect the transformation?
5. If $ h(x) = -f(5x) $, what additional transformation occurs?

**Tip**: Horizontal compressions and stretches depend on factors applied directly to $ x $, and they are often the inverse of what they appear.

Use the graphs of $f$ and $h$ to describe the transformation from the graph of $f$ to the graph of $h$.

$f(x) = -2x - 2$

$h(x) = f(5x)$

Explore the transformation from the graph of f(x) = -2x - 2 to h(x) = f(5x). This involves a horizontal compression by a factor of 1/5, bringing points closer to the y-axis. Perfect for students in Grades 9-12 studying function transformations.

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